I have/had the same issue with Morgan turning right.
Can she step under correctly (ie cross her inside back leg under her belly infront of the outside back leg) with ease on the ground?
Morgan can do this but is much more supple going to the left than the right. He tends to not bend correctly through his whole body and seems to have his rib cage or nose pushing out in the opposite direction. Just like you and I are right or left handed, horses are too!!!
When I ask under saddle he has to think about how to move with me in that direction and is not able to do it with the ease he does when he turns left. It is nowhere near as fluid.
So he tends to resist turning right unless I insist and then he is braced.
So you might find your answer on the ground?
With Morgan I went back to asking him to bend softly first whist standing from just a lift of the rein. Even this made him brace, so I used my hand stretched out for him to turn and target and then put the rein aid back into an open rein. I added a brush with my leg by his girth (and he prefers to bend around my leg rather than have my hand ask). So I ask with body/leg and then follow with lifting rein.
This worked for us and I am sure you can figure out what might work for you. I do think the key lies though in the left/right and more conditioning and doing/practicing on the tough side definitely helps