They're both at fault. If my kid is loud enough to inconvenience other people and she wouldn't calm down, I'd take her somewhere else or just go home.
On the other hand, if I was the manager, I would have talked to the parent and asked her to calm the kid down or take it somewhere else. You don't really shout at someone's kid if the parent is right there. You have a problem with the kid, you confront the parent (if they have a problem with people confronting them over their kid's temper tantrums, then that's on them - they either need to find ways to control the kid or deal with the consequences. If they can't do either, then they shouldn't be parents.)
