Moms shouldn't freak out if another adult corrects their child.
Yesterday, at a crowded playground. A bunch of kids were playing on that metal spinner thing (not sure of what it's called but a bunch of kids sit on it and usually one or two kids spins them around).
Anyway, four or five kids were packed on to this thing and there was a young girl spinning them. She was spinning them quiet fast and a few of the kids started screaming for her to stop so they could get off. The girl was not slowing up, in fact she thought this was funny!!
Her mother was less than ten feet away on a bench doing nothing to stop her. Eventually, another mother walked up to the girl, gently placed her arm on her should and said something along the lines of "please stop you're going to make the kids sick." WELL, THIS got the little girls mothers attention. She flipped out! Yelling screaming, "don't touch my child" "she did nothing wrong" "I can handle my kids" ect. And what shocked me even more was that three or four moms got up and AGREED with her!!
I'm sorry I understand it's a scary world we live in these days but this was another child's mother simply doing you a favor. Your daughter was being a little brat and now she will continue to be a brat because she sees mommy will stand behind her when she does something bad.
Personally, if someone, be it a teacher, a parent grandparents, corrects my child, for a legitimate reason, I give them full permission to do so. Children need to learn to respect their elders and they need to realize that their are rules EVERYWHERE they go, and they aren't always the same as mommys rules. Sometimes you aren't going to agree or like them but you have to follow them or else their will be repercussions.
What happens when your kid goes into the work force and they don't agree with work place policy? Are you gonna come in and tell their boss off for them? No. They won't be able to hold down a job because they don't like the rules.