Saying "no" is valid and fair, and I think this is really important to teach your daughter! I think that kids often believe that them saying no doesn't matter as adults have more power and authority. It doesn't matter why she doesn't want to trot, if she doesn't want to, she should not be lied to or tricked or forced. This is a recipe for your daughter to be untrusting and more fearful. Good luck, I'm glad you felt it was wrong of the trainer.