quick question- do you mean counter cantering or cross cantering? My gelding had a small issue with cross cantering for about a week, lots of transitions fixed this. It kind of sounds like you're describing counter cantering which I have no advice on!! However your pics are gorgeous and I agree with anebel about seeking professional advice (which it sounds like you're doing with a trainer...)
I had a quarter horse who was lazy and often did not change leads in the rear while doing figure 8's. Could happen in either direction. No soundness problem. Just plain lazy.
You really have to cue with shifing your weight and using your leg to get them to change if they are just lazy. Use your crop in the rear to get the horse to wake up and not be lazy.