As someone who’s fiance is studying to become a personal trainer, and as someone who is terrified of him having clients like you (and I mean that in the nicest way possible – I’m sure you’re a nice person, but that situation is horrible), please find a new trainer.

If he is in a relationship, and you know this – but you’re encouraging this situation to continue, it doesn’t say much for your own values and morals.
It probably hurts for you, but just put yourself in her shoes, because I’m sure it wouldn’t be such a nice feeling…
Also, think of the reality of this: if he magically falls for you and leaves her, and you two end up together… What’s to say he wouldn’t do the same to you when the next “strong connection” comes along? Because, believe me, someone else WILL come along. And if he’s the type to leave his girlfriend to go after a “strong connection” like you, then that doesn’t say much for him either.
There are over 7 billion people on this planet, and plenty of them are available. Try finding one of them instead of someone who’s already in a relationship. I could never understand women, and men, who try to get into a romantic relationship with someone who is in a relationship with someone else. Even emotional cheating is wrong regardless of whether or not you cross physical barriers. It reminds me of spoiled children who acknowledge that another child has something of value, so they long for it and try to steal it. Very unsettling.

And for the record, it’s his job/career to be supportive and push you to reach your goals. You’re paying him for that.