Is it illegal to not have an air conditioning unit in a gymnasium?

This is not against the law but I agree with you completely- this is not fair to the girls. I assume the lack of a/c is as a cost saving measure but they could have a unit only running when the girls are practicing . This is a very demanding training and perhaps the people at the community center are not aware how arduous it is. Don't give up and I hope you perservere.