#1 Hell no! You are not over reacting. They should've never done that. That will sit on her mind forever. Things like that can socially scar a child, especilly a girl.
#2 I would have a talk with the director, expressing your feeling on the situation. They need to appologize to your daughter, and explain to her why they put those gloves on her, even after you spoke to them. It will show her that it is ok to handle humilation and recover from it. It will also show her that she is not a freak, and that people shouldn't be afraid to play with her. Once that is done, and she feels better about herself. Take her to another day care.
I know it is not on the same subject, but I was sending my son to a prep school, paying a lot of money, and putting my trust in that school. My step daughter had gone there and came out very smart. The second day there, I get an accident report. Saying that my son got in the way of a flying metal car, and it hit the back of his head!!!! what!!! Day after that, another report, saying that he and another boy, the same boy that threw the car, were fighting over some trains. Following day, another report. After ther first two reports, I had a talk with my son, asking him what was going on. Mind you, he is two, but a smart one. He told me he didnt like school anymore and didnt want to go. This coming from a kid that woke me up the first day of school because he couldnt wait to go there. The third report said that he had pushed the same little boy that was messing with him, causing the little boy to fall on his face and scuff his chin. When I had my talk with my son, I told him that if anyone was hurting him to tell them to stop, and if they didnt to push them away if they were hurting him. That little boy was stepping on my sons hands while he had a car in them. There were shoe marks on the back of his hand and a cut inside. So my son pushed him to make him stop and went to get the teacher. But the teacher had only seen the little boy falling.
I had a sit down with the owner of the school. Told her that I did not think a place should be run like this. The teacher was overwhelmed with 22 kids in a room made for 12. I told her that I understand kids are kids and will fight, but this was unacceptable, and I was taking him out. I got up and went to get my son from class, and he was crying. He couldnt have been happier to leave.
Your daughter will make friends anywhere she goes.