Compassion in place of Confrontation

Since my experience viewing the over whelmed mother in the Chinese take out restaurant, I have contemplated how modern society views violent actions, situations that need to be different, how we handle differences and all the many levels of disagreement.
I have been checking my own actions and know that when confronted in an antagonistic manner, I feel backed up against the wall and my first reaction is to come out fighting, not physically, but with some level of reaction.
It's not the reaction I want to feel, but it seems to be the one that surfaces when I am pushed, made to feel that someone is treating me unjustly, unfairly, or with disregard for who I am.
I have thought about how people have commented that speaking to the woman, so overwhelmed by mothering two small ones, or perhaps that is the only way she knows to react, at any rate we all know that when we confront someone in such situations, it can backfire on us. The person becomes so irritated, so angry, that later the child or who ever is the focus of this persons rage, may be abused even more.... but then I thought.... what if it was Christ, Buddha, the Dalai Lama, Mother Teresa, or some other person of extreme compassion that went up to this woman... I am betting their very presence would defuse and calm the mother. I am certain they would know what to say, how to approach and what's more, have such a demeanor about them that what they said or did, words spoken or not, would melt away the anger. So, is it our very demeanor, our own persona that offends someone who is in a fit of anger ?
Could we not be calmer, so filled with compassion that we would never be taken as being confrontational ? Are we so used to confrontation, even in the grocery store, driving our cars, waiting on the phone, etc that we are not able to approach with total compassion ? I suspect so. Perhaps we should calm ourselves in order to be able to calm.
It certainly has given me much to think about. My own reactions to some very annoying people have fallen so short of compassion. Perhaps we need to be childlike in our approach, simple, no agenda, no confrontational attitudes, just a deep sincere desire to end the suffering of others.

Tiny little feet