Several people have given you the suggestion that works for me 100% of the time. Make the right thing easy. ALWAYS. So, if your horse MOVES AT ALL when you try to mount-fine. MAKE HIM MOVE. Now and fast. Do a few cicles around you, then try to mount again. Same drill over and over until he gets it. It is easier to stand than to have to run his butt off. And after you are on-take your time and make him stand until you are ready.
Sounds to me like this horse respects the trainer, and not you, which is why he stands for the trainer.