Yipppeee! I've just had a breakthrough on this!! Couldn't or wouldn't canter right (lovely balanced counter canters left lead ). Started off as a slight balance problem on his part but we had worked on that with physio\massage and suppling on the lunge so that he cantered left or right on the lunge but I still had a problem when riding - err so guess who was causing the problem
Turns out that there were 2 problems (well 3 if you count being crap at telling left from right lead )- initially I was tensing and 'grabbing' with legs and hands on the right canter -because of our initial right canters turning into unbalanced bolts (talk about horses getting bad habits what about riders!!

)
My instructor forced me to canter without reins (on the buckle) and release my legs and we came up with a really ugly way of asking for right canter (jacknifing poor horse, since he's so clever at counter canter) and I was forbidden to canter on the left lead - note on the board so everyone knew and yelled at me if I was seen on the wrong lead.
As I practised with the relaxed,on the buckle canter I could also evaluate my transitions. I reduced and then eradicated the ugly forced right lead transition request we'd worked out when I realised that I was relying totally on my outside leg when going right - my horse was waiting for the correct aids, including inside leg for strike off and so always cantered left lead.
Now cantering is a pleasure (for both of us - I swear he sighed when I got it right) and improving all the time.