I noticed that in the case of metta bhavana, I seem to generate a lot of compassion while sitting, but as soon as I am in the real world I sometimes react impatiently or with irritation. The same goes for mindful breathing, where I act in daily life without much mindfulness despite effective sessions.

What is the best way to bring the benefits of meditation into every day experience?

One can think of any sitting practice as though it were preparation for using those skills in daily life. One way of translating Mindfulness is "to remember", so practice remembering to return to the present throughout the day, via a chosen object of attention.

Some set a clock to remind them once an hour, others put little notes around the house to remind them. Certain activities lend themselves to easy extensions of your sitting practice, like walking to your car, washing dishes, walking the dog, exercise, etc. - all can be done with mindful awareness. Just be with the sensations of whatever you're doing fully, without letting the mind wander. Be aware of the mind and things you know will trigger unwholesome formations, like getting cut off in traffic. You know it will happen, be ready for it and arm yourself with a mindful and compassionate response beforehand.

It's a habit, and takes time and effort to develop. Every little bit helps, and don't be discouraged at first if you forget. Don't make it stressful, keep it light and rewarding. Relax and release.

Maintaining this mindfulness or compassion throughout your day will increase the benefits of your practice many-fold, and you'll find your sitting practice reflecting that by having deeper sessions with sharper mindfulness.

Good luck!

The following chapter from Yuttadhammo Bhikkhu's book "How to Meditate" should answer your question very well. It applies to lay people.

TL;DR

I will summarize it below:

• Practise the five precepts heedfully


• Eat in moderation


• Consume entertainment in moderation


• Social networking and socializing should be done in moderation


• Sleep in moderation


• Avoid any kind of addiction


• Practise some amount of mindfulness in daily routine activities and motions


• Practise some amount of mindfulness of sensations i.e. acknowledgement of sensations

Quote:

Chapter Six: Daily Life

At this point, instruction in the basic technique of formal meditation
practice is complete. The teachings in the previous chapters is enough
for a new-comer to begin on the path towards understanding reality as
it is. In this final chapter, I will discuss some of the ways in which
the meditation practice can be incorporated into daily life, so that
even when one is not formally meditating one can still maintain a
basic level of mindfulness and clear awareness.

First, it is necessary to discuss activities that are harmful to one’s
mental clarity; activities one must avoid in order for the meditation
to bring about sustained positive results.

As I explained in the first chapter, “meditation” is the mental
equivalent to “medicine”. When taking medicine, there are certain
substances one must avoid; substances that will either nullify the
positive effects of the medicine or, worse, combine with the medicine
to create poison. Likewise, with meditation there are certain
activities that, due to their tendency to cloud the mind, have the
potential to nullify the effects of the meditation or, worse, pervert
one’s understanding of the meditation, causing one to cultivate
unwholesome mind states instead of wholesome ones.

Meditation is meant to cultivate clarity and understanding, free from
addiction, aversion, and delusion, and therefore free from suffering.
Since certain bodily and verbal acts are intrinsically tied to
negative qualities of mind, they are considered ‘contraindicative’ to
the meditation practice; they have an effect opposite to what is
desired, cultivating defilement instead of purity. Meditators who
insist on engaging in such behaviour will face great difficulty in
their practice, developing habits that are detrimental to both
meditation practice and personal well-being. To ensure the mind is
perfectly clear and capable of understanding reality, certain
behaviours must be taken out of one’s “diet”, so to speak.

First, there are five kinds of action from which one must refrain
completely, as they are inherently unwholesome: [Note1]

1. One must refrain from killing living beings. In order to cultivate one’s own well-being, one must be dedicated to well-being as a
   principle, refraining from killing any living being, even ants,
   mosquitoes and other living beings.




2. One must refrain from theft. In order to find peace of mind, we must grant it to others as well; stealing is a denial of this basic
   right to security. Further, if we wish to be free from addiction, we
   must be able to control our desires to the extent of respecting the
   possessions of others.




3. One must abstain from committing adultery or sexual misconduct. Romantic relationships that are emotionally or spiritually damaging to
   others, due to existing commitments of the parties involved, are a
   cause for stress and suffering and based on perversion of the mind.




4. One must refrain from telling lies. If one wishes to find truth, one must avoid falsehood; intentionally leading others away from the
   truth is harmful both to oneself and others and incompatible with the
   goals of meditation.




5. One must refrain from taking drugs or alcohol. Any substance that intoxicates the mind is obviously contraindicative to meditation
   practice, as it is the antithesis of a natural, clear state of being.

Complete abstention from these activities is necessary if one wishes
for meditation practice to be successful, due to their inherently
unwholesome nature and the invariably negative effect they have on the
mind.

Further, there are certain activities that must be moderated or they
will interfere with meditation practice. These are activities that are
not necessarily unwholesome in and of themselves but will nonetheless
inhibit clarity of mind and lessen the benefit of the meditation
practice when undertaken in excess. [Note2]

One such activity is eating; if one wishes to truly progress in the
meditation practice, one must be careful not to eat too much or too
little. If one is constantly obsessed with food, it can be a great
hindrance to progress in meditation since not only does it cloud the
mind, over-eating leads to drowsiness, both in the body and mind. One
should eat to stay alive rather than stay alive simply to eat. During
intensive meditation courses, meditators eat one main meal per day and
suffer no negative physical consequences as a result; whereas the
positive effects of such moderation are clarity of mind and freedom
from obsession over food.

Another activity that interferes with meditation practice is
entertainment – watching movies, listening to music, and so on. These
occupations are not inherently unwholesome but can easily create
states of addiction when undertaken in excess.

Addiction is a form of insobriety in a sense, since it involves
chemical processes in the brain that inhibit clear thought and clarity
of mind. Since the pleasure that comes from entertainment is momentary
and unsatisfying while the addiction and obsession carry over into
one’s life, a serious meditator should determine to make the best use
of their short time in this life by cultivating peace and contentment,
rather than wasting it on meaningless activities that don’t lead to
long term happiness and peace. If one wishes to find true happiness,
one must therefore moderate one’s engagement in entertainment.
Socializing on the Internet and similar activities should be
undertaken in moderation as well.

The third activity one must moderate is that of sleeping. Sleeping is
an addiction that is often overlooked; most people don’t realize how
attached they are to sleep as a means of escape from reality. Still
others become insomniac, obsessed with the thought that they are not
getting “enough” sleep, leading to increased stress levels and further
difficulty in falling asleep.

Through the meditation practice, one will find that one needs less
sleep than before since one’s mind will become calmer. Insomnia is not
a problem for meditators since they are able to meditate even in the
lying position and keep their minds free from stress. People who have
difficulty falling asleep should train themselves to watch the stomach
rise and fall, noting “rising”, “falling”, all night if necessary.
Even if they are not able to fall asleep (which is unlikely, given the
calm state of mind while meditating) they will find themselves as
rested as if they had slept soundly through the night.

Finally, it is worth mentioning that to truly gain results in the
meditation practice, a meditator should set aside at least a period of
time to remain entirely celibate, not just avoiding immoral sexual
activity, since all sexual activity is invariably intoxicating and
will be a hindrance towards attainment of mental clarity and peace.

Once one has put aside activities that interfere with clarity of mind,
one can begin to incorporate meditative awareness into ordinary life.
There are two ways in which one can meditate on ordinary experience,
and they should be practiced together, as follows.

The first method is to focus one’s attention on the body, since it is
the most clearly evident aspect of experience. As in formal
meditation, the body is always available for observation, and thus
serves as a convenient means of creating clear awareness of reality in
daily life. Since the body is generally in one of four postures –
walking, standing, sitting, or lying down, one can simply become aware
of one’s posture as a meditation object to bring about clarity of
mind.

When walking, for example, one can note either “walking, walking,
walking, walking” or “left, right, left, right” as one moves each
foot. When standing still, one can focus on the standing position and
note “standing, standing”; when sitting, “sitting, sitting” and when
lying down, “lying, lying”. In this way, one can develop clarity of
mind at any time even when not practicing formal meditation.

Further, one can apply the same technique to any small movement of the
body – for instance when bending or stretching the limbs, one can note
“bending” or “stretching”. When moving the limbs, “moving”. When
turning, “turning”, and so on. Every activity can become a meditation
practice in this way; when brushing one’s teeth, “brushing”; when
chewing or swallowing food, “chewing, chewing”, “swallowing,
swallowing” and so on.

When cooking, cleaning, exercising, showering, changing clothes, even
on the toilet, one can be mindful of the movements of the body
involved, creating clear awareness of reality at all times. This is
the first method by which one can and should incorporate the
meditation practice directly into ordinary life.

The second method is the acknowledgement of the senses – seeing,
hearing, smelling, tasting and feeling. Ordinary sensory experience
tends to give rise to either liking or disliking; it therefore becomes
a cause for addiction or aversion and ultimately suffering when it is
not in line with one’s partialities. In order to keep the mind clear
and impartial, one should always try to create clear awareness at the
moment of sensory experience, rather than allowing the mind to judge
the experience according to its habitual tendencies. When seeing,
therefore, one should know it simply as seeing, reminding oneself
“seeing, seeing”.

When hearing a sound, one should likewise note “hearing, hearing”.
When smelling pleasant or unpleasant odours, “smelling, smelling”.
When tasting food or drink, instead of becoming addicted to or
repulsed by the taste, one should note “tasting, tasting”. When
feelings arise in the body, hot or cold, hard or soft, and so on, one
should note “feeling, feeling” or “hot”, “cold”, and so on.

Practicing in this way, one will be able to receive the full spectrum
of experience without compartmentalizing reality into categories of
“good”, “bad”, “me”, “mine”, “us”, “them”, and so on. As a result,
true peace, happiness and freedom from suffering is possible at all
times, in all situations. Once one understands the true nature of
reality, the mind will cease to react to the objects of the sense as
other than what they truly are and be free from all addiction and
aversion, just as a flying bird is free from any need for a perch on
which to cling.

This then is a basic guide to practice meditation in daily life,
incorporating the meditation practice directly into one’s life even
when not formally meditating. Beyond these two methods, one can also
apply any of the objects discussed in the first chapter – pain,
thoughts, or the emotions. The techniques discussed in this chapter
should be thought of as an additional means of making the meditation
practice a continuous experience whereby one is learning about oneself
and about reality at all times.

This concludes the basic instruction on how to meditate. Remember that
no book, no matter how detailed it may be, can substitute sincere and
ardent practice of the teaching itself. One may learn by heart all
wise books ever written and still be no better off than a cowherd
guarding the cattle of others, should one not practice accordingly.

If, on the other hand, one accepts the basic tenets included in a book
like this as sufficient theoretical knowledge and practices sincerely
in accordance with them, one is surely guaranteed to attain the same
results as countless others have likewise attained – peace, happiness
and true freedom from suffering.

Notes:

[Note1] These five behaviours correspond with the five Buddhist moral
precepts.

[Note2] The following is in accordance with the eight meditator
precepts normally taken by Buddhist meditators on holidays or during
intensive meditation courses, adding the three precepts below to the
five above and undertaking total celibacy.

The purpose of a sitting meditation session is that one continues the practice for the rest of the day.

Following 4 factors, though used in a slightly different context in the quoted text, may help in trying to extend your practice to daily session:

1. Concern (ābhoga): you pay initial attention to the breath, you apprehend the breath, you advert the mind towards the breath, to the effect: ‘I will try to make the breath tranquil.’




2. Reaction (samannāhāra): you continue to do so, i.e. you pay sustained
   attention to the breath that way, do it again and again, keep the
   breath in the mind, to the effect: ‘I will try to make the breath tranquil.’




3. Attention (manasikāra): literally ‘deciding to make the breath tranquil’.
   Attention is the mental factor that makes the mind advert towards
   the object. Attention makes the mind conscious of the breath and
   know the breath.




4. Reviewing (paccavekkhaBa): you review (vīmamsa) the breath, make it
   clear to the mind, to the effect: ‘I will try to make the breath tranquil.’

p35/36 Knowing and Seeing by Pa-Auk Tawya Sayadaw

In the context of your question:

1. Concern - one should be concerned to retain the object of meditation may it be breath or metta


2. Reaction - one should see if one's mind is with the object and if not bring it back. Even if not periodically are apply your mind to the objects by trying to see the meditation object (in the case of breath / ) or be with the meditation object.


3. Attention - one should pay attention to what the mind is doing, i.e., wandering off or staying in focus


4. Reviewing - periodically are checking if you are at it

Also, you can try extending to other Brahmavihara meditation to remove impatient reaction and irritation as they can be not only due to ill will but due to other factors like cruelty, discontent and aversion. E.g. one sees someone with a better car which might be irritating. Something being better than mine give arise to discontent.

(1) Rāhula, practise the cultivation of lovingkindness. For when you cultivate lovingkindness, any
ill will will be abandoned.

(2) Rāhula, practise cultivation of compassion. For, when you cultivate compassion, any cruelty
will be abandoned.

(3) Rāhula, practise the cultivation of gladness. For, when you cultivate gladness, any discontent
will be abandoned.

(4) Rāhula, practise the cultivation of equanimity. For, when you cultivate equanimity, any
aversion will be abandoned.

Mahā Rāhul’ovāda Sutta