Overly modest
I am chiming in late and you will not like me but BEFORE I read your SWH and other comments, my impression from your comments which included cupping a "private part", makes you cringe to think about someone touching your bottom. Overly Modest.
This is gymnastics. Coaches are doing their job to make sure the form is correct because if one of those little girls stretches improperly and ends up with an injury, then the parents would be all over the coach for not making sure everyone was in the correct form. A piece of foam will not help the form because the couch would not be able to make sure it was correct if the coach is forbidden from touching the child.
No, you did not say "feel them up" yet it was clear from what I read that it was a thought that possibly ran through your mind.
There are a lot of jobs out there where someone is touched in a completely innocent and professional manner... Doctors, Massage therapists, physical therapists, etc.
Please don't bring attention to this as "bad" for your child. It will only set her up for anxiety issues every time a coach, Dr, Massage therapist, etc ever try to help her.