I wouldn't say DON'T go to a BHS clinic, but I would say that
1) talk to her coaches about it first. they might have a better alternative.
and
2) if she does go, as SOON as she learns the skill, have her start working on them in HER gym with HER coaches so they can teach the form, otherwise she will be practicing it with bad form and that will be a bad habit to break and in the long run she will end up learning the back handspring CORRECTLY *later* than her teammates (even if she can do the skill itself sooner).
As for me, I was an assistant coach but not great with the form end of things. I just had a knack for teaching the mechanics of a skill and helping kids get it faster. Soooo... *ducks from the coaches here* I taught her a back handspring on our trampoline at home when she was ready. As SOON as she could do one (within a week), I told her coaches and told them that she would like to work on them but that I didn't want her to do them at home because I didn't want her to develop bad form habits. They started doing privates with her once a week. She's now doing them on a mat and working toward doing them on the floor. She's also level 2.
(I agree with other posters though that you need to have other skills going into a back handspring or your child can get hurt. They also have to have the strength and coordination to do the skill)