So for myself, I need to strengthen my leg (it likes to move too much and swings back) and my upper body/arms. I know of the exercises on the horse (no stirrup,two point), but is there anything I can do off the horse that will help? Preferably to help my leg situation.
Crunches over an exercise ball or "the plank" for strong core muscles. If you do hunters a recumbent bike is great for strengthening the muscles in the back of the leg which really help with a good secure two point. If your whole leg is strong you'll be less likely to pinch with your knee and swing that leg back.