A Painful Lesson for Me

I am ashamed of myself, disappointed in myself. I try not to ever have to say such things but today I am saddened over my failure to react.
I was waiting for my vegetable fried rice order at our favorite Chinese take out place, and there was a young mother of two, one child was probably close to 2 in age, the other one, probably about 4. The 4 year old was a brat, plain and simple. Crying and screaming because he wanted the chair his mother was sitting it, but the mother was making it worse, she was nasty, plain old ugly with this child. Finally her order was ready, she paid and got up to leave, the smaller child in her arms. The 4 year old grabbed the chair and started saying, "my chair, I got my chair." the mother then said, "fine, you have your chair now keep it" and walked out the door. The little boy of course ran crying after his mother, fearing she would leave him. He came within a centimeter of being squished by the big heavy door of the business. He ran across the busy park lot towards his mother who at this point grabbed him by the arm and how that child's arm did not become dislocated I will never know. Anyway she then threw him in the car and proceeded to slap him, hit him and scream at him.
What is almost more disturbing than this is that I stood there in the shop, doing nothing. I thought about how if I had a cell phone I would have called the police, but why oh why did I not walk over to her in while she was waiting for her order and tenderly and calmly ask if there was anything I could do to help. To explain to her I understand the stress of having two little ones etc ? Why then didn't I just tell the people in the take out place I would be right back, they know me, so its not a big deal and go and help this young woman with her children, to calm the situation down ?
You see, this one is not a do over. Some things in life we get to do over. But this is not one of them. This little child had to experience all this anger without one single calm adult watching this incident unfold without offering to help. Sure, this child no doubt experiences this type of anger regularly, it showed in the way the little one behaved. But what if I could have prevented this one time of violence for him ? Isn't one less beating better.
I am ashamed of myself. I failed to show compassion. Please don't tell me I am being hard on myself or to not beat myself up over this. I am not beating myself up, just disappointed in my lack of help for an innocent. I should be, we all should be when we pass by the opportunity to spare someone from being attacked, be it by a parent, a spouse, or a stranger. If I don't realize my own mistake, I will make it again some time. If I don't share my mistake, then the pain of this lesson goes on without a purpose at all.
We are to be merciful and compassionate