I feel like you may be jumping just slightly ahead of him... but then when I watched the videos a few more times I think what is really happening is that you need to close your hip angle a little more, and stick your butt out more. I think because the trainer has you bring your hands up the neck so far, you tend to want to jump up to your hands a little bit.
I understand what your trainer wants, and lifting your hands and driving will get the horse off the forehand. But you can try lifting your hands literally UP off of the neck, not farther up the neck, does that make sense?
Another reason she may have you do it is if you aren't solid with your crest release yet, to avoid having the horse bumped in the mouth in which case I understand why she's having you do it, just try not to push yourself up to your hands so much, bring your butt back more and close your hip angle.
"The white horse moved like a dancer, which is not surprising: a horse is a beautiful animal, but it is perhaps most remarkable because it moves as if it always hears music."