A Parking Lot, A Hairbrush, and A Little Boy

I am disappointed in myself.
Today, I was heading to my car from a playground where I was taking some pictures, when I heard a voice in the parking lot. It was a mother, a horrid one, scolding her child who was no more than two, for crying. "I've had enough!" she yelled at him, "Where's my belt? I'm gonna find my belt," she claimed, while she riffled through her big weapons bag while her son stood whimpering next to her.

She couldn't find her belt apparently, because she decided a hair brush would do. While smacking him on the back of the legs a few times and snarling at him for crying, I approached closer, wondering if I should say something. As I got to my car, which was right next to them, I burned the back of her head with the lasers coming out of my glaring eyes and opened my trunk to put my gear in with a body language which said, You horrid person, are you crazy? You are not a good mom.

I dared myself to say to her, "I'd cry too is someone was hitting me with a hairbrush" or "You do realize that's assault with a weapon? Hitting someone with a tool like that?"
But, I said nothing. Did I fear she'd turn and use the brush on me? Afraid she'd yell at me? Concerned she'd beat the kid harder later, taking it out on him that she was embarrassed in public?
She just hit a child repeatedly with a hairbrush and I did nothing. I said nothing.
I've read stories from adults who were beaten by their parents and never understood why adults around them never did anything about it, even if they knew something was wrong.

I thought about an incident in Boston years ago when a woman was stabbed to death in an alley between two apartment buildings. Many people heard her screaming and not one person made a phone call. Were they afraid? Did they assume, with so many other apartments around them that someone else would surely call?

I had a crowd mentality today and I was a crowd of one. No one else was there to say something. I was it.
I began to leave but was too upset. I thought maybe she was going to sign him up for the pre-school program at the rec center, so I went in, hoping to find the woman who runs the place, who I've come to know, and ask her to keep an eye on that kid and his crappy abusive mother. But, no, she was sitting in line with a group of people waiting to get help on her taxes. (I hope she owes a ton). Then, I saw an empty sheriff's cruiser in the parking lot and thought, maybe there's one inside and I can just ask him - As a citizen, what can I do about that?

In my daydream, the sheriff's deputy goes up to the woman and chastises her. But, I can't find the deputy.
It occurs to me now that I should have left a note on her car. Would it have stopped her from being a total jerk? No, but at least I wouldn't feel like I did nothing for that poor little kid. Here's hoping he eats his Weaties and kicks her ass once he's big and strong.
Here's hoping I have the guts to say something next time around.