I've been riding my Mom's mare recently, and she only picks up the left lead. I've started many of my own young horses and have some"tricks" to help young horses pick up the correct lead. However none of these things work with this mare. Unlike my young horses I don't think this is a matter of balance I think it's a strength issue.
What exercises would you recommend to strengthen and encourage her to pick up the righ lead?
Is the inside hind or outside hind that I need to work on?
Vet first, then the strengthening exercises. You need to know exactly which muscles,ligaments or tendons are involved first. Well worth the exam when you think of the cost of keeping a horse and the time involved strengthening a horse.
I had similar issues with my mare when I first got her. She's an OTTB, so it perhaps wasn't too surprising that she had an easier time in one direction.
In the beginning I didn't do a whole lot of canter. Instead, I went back to walk and trot, working on balance and keeping a consistent rhythm. We also did a lot of transitions, stretchy circles, changes of pace within a gait, etc. When that was going pretty well, we introduced a bit of easy lateral work like leg yields, shoulder-fore. When we went back to the canter, it was so much better than it was before all of these other exercises.
One other thing that helped in my case was to make sure my horse is doing a really nice and relaxed trot before going into a canter. I also try to do it on a slightly smaller than 20m circle, then leg yield out, sit and ask. If she doesn't know it's coming and thinks we are just doing a relaxed trot, then the canter usually comes in a very relaxed and balanced fashion.