Balance problems with riding?

I have a bad knee on my right side, I'm not sure why, but it used to give be problems even back in high school in gym class. I've noticed that when I ride my balance is always off and I never feel secure in the saddle. I always put too much weight on my good leg, and whenever I feel my balance off and realize what I'm doing, I make it even worse. Does anyone know of a way to fix this? I'm not sure, but maybe exercises or something? I ride Western and Aussie, I've never tried English.