Just playing devils advocate but what does your HC know? If I am the coach recruiting your DD I am going to ask her who her HC is and if I don't know him try to understand what they teach.
It will be stressful for the me if the HC is teaching something that is at odds w/what I teach.
That's a fair question. I'm not saying this it's right or wrong for a player to see things this way, just pointing out how my DD sees it.
Most recently, I have been her hitting coach. She realizes that it's not going to work to be on a team where the coach is actively trying to change something that she doesn't believe should be changed. On her last team, the coaches wanted to change her to a no-stride approach, change her grip and stance (even though she led the team in batting average and extra-base hits). They didn't ''actively'' try to change her, just suggested it for a spell, so there was no issue. But if they had insisted, that would've been a problem because she would've felt conflicted between what she and I believed and what her coaches believed.
There also was the case I mentioned in the OP - the coach who wanted her to swing down and cut under the ball. That was a deal-breaker. It wasn't just me. It was her.
But I can see your point of view and how she (and me, her dad) might raise red flags for you as a coach. But keep in mind that she would be open-minded to many changes in her hitting. But there are some changes where she and I would draw the line. And she and I would be willing to be up front about that to the coach.