This has been a very interesting thread to a novice of pitching. Thanks to all involved.
I'll leave the "slap", or "not to slap" to the experts. I will say that if I'm paying for pitching instructions, a coach isn't going to FORCE a mechanical change to her pitching. If they want to make suggestions, that's completely fine. This mindset of "I don't like it so I'll force them to change it.", is completely ludicrous. It's that God-like personality that too many coaches have.
Maybe I'm misreading what you're saying. Are you speaking to the glove slap specifically? If so then yeah, it's not something to worry about one way or the other in my opinion.
If not, then I would say if the coach is FORCING a mechanical change on the pitcher then you didn't do a very good job of vetting that coach in the first place. You should WANT your daughter to learn whatever that coach is teaching. If you want the coach to let her do it the way she wants then you're wasting your time and money on lessons. She already knows how to do what she does.
The first, most important step in learning anything is a willingness to change - if change makes sense.