Sounds like the chiropractor stuff other people mentioned. I have a video of her cantering, not me riding but this is what she does if anyone wanted to see if they saw anything that stood out particularly. http://www.youtube.com/watch?v=SRb5s3wnqgk
She looks like a sweet horse. A more independent seat with a stable, supporting leg and less hand from the rider would probably be really helpful for the horse to stay in the canter. My suggestion would be to have the rider practice two point without stirrups at the walk and trot to get both the horse and rider more fit and balanced.
Meh the rider is not great but that is not causing the swapping. That mare hurts. She is inverted and unhappy but trying her heart out. SI is my guess- just a guess. She looks to be so tight over her back that the rider has nowhere to sit.