@glitterbag,
Actually, I'm surprised whoever was at the front of the line didn't offer to let the mother of the screaming child go ahead of her, so she'd get the kid out of the store faster. That's what I think I might have done if I were on the line.
The woman should have gotten her child out of the store ASAP--possibly rapidly dropping her unpaid for items at the customer service desk, and quickly asking them to just hold them, if they were really important to her.
Other customers should not have been forced to endure her out-of-control child, nor should she have over-reacted to a request to quiet the child down. When your child is in that state, in a store or restaurant, you really have to remove them from the situation and deal with it privately, both for the child's sake, as well as for the benefit of others who are being disturbed by the child's unruliness.
I don't think the other woman made an unreasonable request. Just following that other woman to her car, let alone punching her in the face, are both very inappropriate, and the mother and child may both have serious anger management issues. In a child, that's part of their emotional and developmental immaturity. An adult has no such acceptable excuse.
There's road rage, and now there's apparently shopping rage too?
I hope they find this woman and hold her accountable for assault. She needs to learn to control herself.