Sankkharas are very deep and take lots of meditation to uproot or remove.

For example (contrary to common ideas), jhana is a sign of a very deep level of purifying sankharas. I just mention this to point out how deep sankharas are and the lengthy process of removal (as described in SN 36.11).

I think without lengthy dedicated full-time practise, it is difficult to manage sankharas.

It seems your mind is calm during meditation. Is it or is it not?

Now listen carefully my friend.

The truth about sankharas is very deep. Only those whose mind is totally calm, can penetrate enough into it to grasp it.

So pay attention my friend.

"When my mind wonders I note thinking thinking or seeing seeing etc then I come back to the breath."

First obstacle: mind should not wonder.

First, you need to establish enough concentration, so that your mind is EASILY and WITHOUT ANY EFFORT anchored to the breath.

Once your mind is easily and without ANY effort whatsoever anchored to the breath, your mind will not wonder.

You must master this "easy and effortless no wondering of the mind" first, before moving forward into removing sankharas.

So, I tell you. The path to removing sankharas is to first achieve this extraordinary level of concentration that I explained.

Can you do that? If yes, you're ready for the next steps.

"To rewire the brain and remove sankharas am I meant to just notice sensation and not react? So someone cuts in front of me on the road and I feel a strong sensation of anger begin to arise. So I just watch it and know that it's anicca, Dukha , Annatta? And wait for it to pass? I must do this with all sensory inputs when I feel triggered? And then sankharas will be removed eventually? Is this correct?"

No, not correct. It's much easier than you think.

Once sankharas are understood, seen, penetrated, explored, seen their cause, it is much much easier than you wrote above. It's like moving a finger. So if someone cuts in front of you, you "move a finger", and no anger will arise in you. Your anger will depend solely on your decision. Any feeling that will not be welcome in your mind, will depend solely on your decision. This is the power of wisdom. This is the liberation from suffering the Buddha taught.

The first step of removing Sankhara start when you become a Sotapanna. This is achieved by removing personality view. (Sakkaya Dithi)

This processed has layers.

Root condition. Buddhist training is directed towards eliminating the defilements (kilesaa). The foremost defilements are the three unwholesome roots — greed, hate, and delusion. From these spring others: conceit (maana), speculative views (di.t.thi), skeptical doubt (vicikicchaa), mental torpor (thiina), restlessness (uddhacca), shamelessness (ahirika), lack of moral fear or conscience (anottappa). These defilements function at three levels:

Transgression (viitikkama) leading to evil bodily and verbal acts. This is checked by the practice of morality, observing the five precepts.

Obsession (pariyu.t.thaana) when the defilements come to the conscious level and threaten to lead to transgression if not restrained by the practice of mindfulness.

Latency (anusaya) where they remain as tendencies ready to surface through the impact of sensory stimuli. Security from the defilements can be obtained only by destroying the three roots — greed, hate and delusion — at the level of latency. This requires insight-wisdom (vipassanaa-paññaa), the decisive liberating factor in Buddhism.

http://www.accesstoinsight.org/lib/authors/mendis/wheel322.html#causality

I think instead of asking how to remove sankharas, we should ask how to purify the mind and develop the mind, which is a gradual process that includes not only meditation but also other aspects of the Noble Eightfold Path.

In this answer, I quoted the Lonaphala Sutta, which teaches that similar to salt crystals placed in a cup of water being salty, compared to the River Ganges, one who performs unwholesome actions would barely experience the effects of it, if he is "developed in the body, developed in virtue, developed in mind [i.e., painful feelings cannot invade the mind and stay there], developed in discernment: unrestricted, large-hearted, dwelling with the immeasurable".

So, it is this kind of development in body, virtue, mind and discernment that is needed.

Ven. Yuttadhammo in Chapter Six of his How to Meditate booklet, states:

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.

Further on, he recommends development of virtues starting with the five precepts, and also moderation in eating, sleeping and entertainment. Beyond the five precepts, virtue (sila) also includes Right Speech, Right Action and Right Livelihood. This answer would also be helpful with regards to the cultivation of virtue.

He continues:

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.

You can read further in his booklet on how to incorporate meditative awareness into ordinary life. There is some information in this answer.

Concerning removing of thoughts - well, the Buddha did not teach to remove all thoughts, but rather remove negative thoughts. In this answer, you can find scriptural quotes recommending to remove thoughts which are based on the three poisons (greed/ addiction, delusion/ confusion and aversion/ ill-will). This applies both during meditation and in ordinary life.

Concerning meditation - I think you already know how it works, but you can refer to Ven. Yuttadhammo's How to Meditate booklet for basic information. If you need advanced information, I think we have other meditation experts here in Buddhism SE, or you can consult a teacher.

Finally, this great answer, tells about Appamada (heedfulness), which is the most important ingredient to all of this. It applies to development in body, virtue, mind and discernment - everything. The Appamada Sutta says "heedfulness is the one quality that keeps both kinds of benefit secure — benefits in this life & benefits in lives to come."

Bringing the mind back to the breath once you recognize that it has wandered away, is part of the practice of heedfulness.

Recognizing negative thoughts or triggers in ordinary life, and dispelling them, before they make you consumed with anger, anxiety or depression, is also part of the practice of heedfulness.

Ensuring that your house doors are locked before you leave your home, is also being heedful, but that's not part of Buddhism.

You can't really remove sankharas, but you can have them wither and fade, as you build new ones. How? By not feeding them with obsessive thinking. The less you think certain thoughts, the more the corresponding sankharas wither and fade.

Now, not thinking thoughts is not a matter of suppression, that's too hard. A more practical way is to find a different perspective, a different system of interpretation, that will change your focus and your attention away from your typical thoughts and onto completely different thoughts.

This is called meditation with discursive support, when you pick a theme for meditation, like a musician picks a theme for improvisation, and then you play by making mental statements within the new frame of reference you're practicing, and letting free associations flow, then making another statement and so forth.

For example, instead of your typical capitalism theme, you think how many people in fact try to help others in most basic ways, and try to come up with some real examples and then think what could motivate people helping others. Just an example.