I need your help please

I have an OTTB who is a wonderful guy. I am scared to death because after having him see four different vets I cannot get a diagnosis. I have owned him for over a year and because he wouldn't run he was put in a pasture and left. The young lady that I bought him from rescued him and made him into an incredible companion. He is seven now , gets good nutrition to include supplements Platnium and weekly glucosamine shots. He was malnurished when she got him to the point that he had very little hair . He is four years out from that experience.

  He has a stall and lots of turn out. He is ridden as a hunter and goes out on trail for enjoyment his and mine. He does this thing with his right hind leg that usually begins with him parking out, (we check reguarly for beans) he rides fine at the walk but at the trot will stop hold his leg to the side and shake it. There is often a clicking sound associated when he moves off but not always. He has had both stifles injected with adequan. I believe the problem to be in his hip. It is as though his right hip joint twists to the side and perhaps slips out of a socket. No vet has been able to witness it because there is no way to make him do it . He can go long periods without a problem but with regular work and asking him to engage his hind end and step under I have the best chance of making it happen. It happens only at the trot and he often prefers to canter. Once the episode is over he walks fine and is not lame. I have spent more money on vet bills than I paid for him.  I had heard that he flipped over in the starting gate when he was younger.I am baffled and have arranged to try a chiropractor and more exrays with a new vet ( this time of his hip area) Anyone have any ideas? Thank you for any ideas you have.

Sincerely,Donna