This is an older thread, but I just came across it. I had a QH Mare that had never cantered, and when she finally learned (at about 15 Y/O) she would not pick up the right lead. She did use the right lead in the pasture, but under saddle, never.
We trotted her fast to a fence at about a 45 degree angle at a spot about 30-40 feet from the corner of the arena (which is to our right). at the fence she was given the canter cue as she made that sharp turn to the right, and made a few strides to the corner and was cued again, turning right. After a try or two, (the important part is to really drive them out of the corner) having made two sharp right turns and being asked to canter at the same time, she got the right lead; It is helpful to have a spotter also so you don’t delay or hesitate leaving the corner trying to feel is she is correct. Your spotter can say “got it” and you keep her in the canter for a while so she gets the feel of it. WE don’t have anyplace to canter very often so we don’t get to practice a lot, but she did finally learn how to pick up the right lead successfully. Hope this helps some.