Have you considered pain as an issue with your
horse? With your youngster being stiff and one sided you might want to
have a chiropractor check her out. I have a "short" 3 yr old (born in late
Aug) and only 13.3H, but she quite willingly canters in both directions when
lounging or being ridden in the arena.
I've also been told to practice what your horse
doesn't do well, rather than what they are already doing well, so for instance,
with my new 7 yr old, he doesn't like his back feet picked up but is okay on his
front, so 90% of my hoof picking & hammering time is spent on his
rears. This new fellow also has a preference to going counter-clockwise, but no
physical signs of discomfort of stiffness, so I keep him going clockwise longer
than he wants to, rather than switch directions before he tries. I watch for the
signal from him that he is considering a switch, then put myself in position to
keep him going the direction that I want.