Ugh! Same problem right here and on the same side! My trainer is constantly reminding me to step down more to the left because I am so secure on the right but I carry much less weight in my left heel and it tends to swing a bit. I've spoken to him and I'm not quite
to where he wants me to do no stirrup work just yet but doing a lot of two-point with the conscious thought in mind to make sure I was putting more weight in that left heel. It's gotten a bit better in the several weeks I've been focusing on it, along with doing exercises off the horse to make sure my muscle tone is even on both sides. I started doing exercises at home and was surprised to find that it was even waaaay harder to do them with my left leg as the right. I have some mild scoliosis in my back so I guess over the years I've always compensated by using my right side more (ironic, as I am left-handed and left-side dominant in everything else).
My Navy husband is really helping me to workout and focusing on getting that left side up to snuff when compared to the right side. I've only been doing the workout for about a week but I already noticed a definite improvement over fences last lesson.
I do lunges while holding weights and squats. Seated I lay on my side and do leg lifts on either side. Also a standing exercise I hold onto the kitchen counter or a windowsill and do leg lifts forward from the hip with my knee bent. Thigh is parallel to the floor and my knee is bent. When I lower my leg I don't let my foot touch the ground. This has helped with strength and flexibility in my hips. You can probably google leg workout exercises or exercises for equestrians to find diagrams and descriptions that do a way better job than I can describe. I'm beginning to learn that my horse-related fitness doesn't end when I climb out of the saddle. I hope it helps!