Okay. So you're having a bad day. The kid is crying and not cooperating. What do you do? You pick the child up, carry him through the store or you leave the store with your child and come back later when the situation is better. Most people know that children throw fits or become uncooperative. Most people are understanding, especially other parents.
Children are not puppies or animals. They are small human beings that are learning how to treat other human beings by the way we treat them.
In this case the mother was arrested. In my humble opinion, she should be forced to take anger management and parenting classes.