How do you discipline in public..?

I was on my break at work, and sitting outside, when a mother and a child (who appeared to be two or three) come out from being inside.

The child was walking a few steps ahead of her, and the mother shouted come here and hold my hand.... Obviously, so she wouldn't run out into the street.

When she took the child's hand, she did start to cry. The mother then told her to "shut up," or that she was going to "whip her."

It was then, that she took a belt out of her purse.

Now, I know how other people discipline their children is none of my business.... But it just made me so sad to think that she potentially uses that belt on this toddler. Even as they continued into the parking lot, I could hear her little screams and the mother shouting at her.

I know that my daughter sometimes acts out in public, and it can be frustrating.... But I couldn't imagine pulling a belt out of my purse . :/