Kind of hard not to leave a hand print, but that goes away. It hurts me a heck of lot more than it hurts them. When your daughters on the floor throwing a fit over hair, sometimes all you got is your hand. Breaking the skin is excessive, and IMO child abuse.
While in the grocery store one afternoon, I was on an isle with a father who was pushing a small boy in a basket. The child was acting horrible. After several verbal discipline attempts, the father started popping legs. Someone actually stopped him. I don't consider that child abuse. I probably would have taken the child in the bathroom so as not to disturb the public, but other than that, nothing wrong with it.