When a horse cross canters or drops a shoulder these may all be symptoms of a back or pelvic issue.
The change in canter is to avoid stress on the hip and sacroiliac. Dropping the shoulder is to aid your horse in lateral flexion ( bending). A subluxation in the low back or SI joint may be the cause. Having a equine chiropractor evaluate your horse will detect this problem. Your vet is not trained in biomehanics to this degree, so they will not spot the cause.
Please contact me at 781-337-1180 or email at indekchiropractic@gmail.com