ESH
Never, ever put your hands on someone else’s child unless there is an imminent threat of harm or property damage. This mother did not ask for your help and did not need your help. The child was not in any danger from going into a restaurant. Maybe he could’ve gotten something to eat.
The mom had every right to give you the side eye. But that is all she did. Your mom decided to pick a fight with her. Also, instead of realizing that she instigated the whole thing, she tries to get the other mom kicked out after it was over. Your mom seems like the type who would get into really bad road rage that could get someone killed.
The other mom for initiating physical contact.