ETA: per your SWH, I would commend her for communicating with you. Good for you for keeping those lines open.., you'll need it in the future. If she prefers not to go back, that's great but I wouldn't just pull her because she did nothing wrong.
Original:
When my daughter was in cheer training with male coaches, I did not drop her off and go on my way. We (moms) stayed and watched from the viewing area.
It's a very expensive sport and I wanted to see what I was paying for. I've been in pricy studios where the instruction was lax and the team just socialized because no parents bothered to stick around to see what was going on.
Tumbling does have a coach spotting the child which involved some touch " professional".
I'd be livid if tickling was a part of the time I paid for and I'd make sure the owner was aware that a coach was tickling the students. I know they'll say it's all in fun due to the strictness in instruction to "lighten things up".
You do realize that some girls on the team may have a crush on the coach. I know my daughter had a coach the girls loved and many would be all huggy with him which was also inappropriate.
Do not make the assumption that this coach is a predator. This behavior is not professional and it does need to be addressed with the owner of the gym.
I would also run his name through the predator site. I know of 3 coaches in the DFW area that were charged with indecent behavior with students.