Squats on the ground, legs at normal distance and horse width. Then do squats on the edge of the stairs with heels down. Do both normal distance and horse width on the stairs (as it works slightly different muscles). Use the banister to balance, and work up the number of sets and reps as you get stronger. Make sure you keep your weight even in both your legs.
You could try staying in a half seat at all gaits. You could also try rising for three beats, sitting for one at the trot. These exercises would force you to have ever pressure on both legs.