My horse who was always auto-swap stopped cantering left. Determined it was arthritis in his neck. Also with OTTBs cantering on a lunge line on small hill can help.
Look into any possible issues in the right hind. The left lead starts with the right hind and race horse often have stifle issues, thatâs where Iâd start if you consult a vet.
Health wise, I agree with everyone with getting your horse checked over. You donât want her in any pain.
Training wise, I would suggest fixing the fact that she doesnât move off your leg first. This can be done at any speed, but I prefer to start at the walk. I like to start on the center line, leg yield to the quarter line then back. Or your can try side passing over a pole on the ground. Donât just work on her bad side. Make sure she works her good side too, as it will help her understand what is being asked.
Do your lunge with side reins? Just because you are lunging on a circle doesnât mean they are going to bend to the inside. If she has been counter cantering on circles a lot, she will have the balance to hold herself bent to the outside and circling.
As for the canter. Get a good trot, with a really good bend, trot a circle in the corner, as you come out of the circle (onto the long side of the ring) ask for the canter, if she does not pick up the correct lead, prepare, and do a square corner (90 degrees). This will usually force the horse to pick up the correct lead.