OP, I think I can understand why the teacher changed you daughter's clothes and that might be because she was seriously worried about her getting too hot.
As the room was warm and she would have been moving around, and had a cardigan on, a vest and thicker tights, she might have dangerously overheated.
I think it was more the whole situation of her being there alone that would have been best avoided..
It was this that meant the only person available to intervene with your baby's too hot clothing was the teacher herself. It is a little like what might have happened had she been at a nursery and needed to be changed by one of the staff there.
I do not mean to attack you OP and I can see why you are very upset and worried over what happened.
But what teaching ideology does mummy-free ballet for a baby come from?
It cannot be a serious one. It's the opposite of suzuki if you see what I mean.
I think 2.5 is way to young to be at a class. It might be different if she was there with you or her nanny and everyone did some dancing and clapping. It should be very light hearted, listening and moving to music.
At a nursery she would be without you or her nanny, but then there would be lots of helpers and she would have been used to it there everyday. Even then it is worrying.
It seems formal and unnecessary for a baby to be in a serious class alone at this age! That would be better for about four or five in my opinion.
Is it really ballet, or is it more music movement and mime? (I am just interested.)