You can try riding bareback but I've always done no stirrup riding to strengthen my leg. Every day do it for alittle bit and make it a game and challenge for yourself.
I havtn ridden since January(horse accident and I'm still recovering) but before my accident I was able to go 25 minutes nonstop of no stirrup and you have NO IDEA how rewarding it is to be able to do a posting trot no stirrup for that long. People are amazed by it, and it's very rewarding and it helps your leg soooooo much. It takes acouple months to get to that point but it helps ALOT.
Make sure you're not pinching with your knees, as that can cause your lower leg to swing around. Do lots of no-stirrup work and really focus on keeping the inside of your calf on the horse and your heels down
I've never had his issue however I have friends who have. I also do a lot of barback riding. Barback helps you to use our core strength and stay balanced and still. Keeping your heels down is a must! Good luck
My lower leg used to move a lot also but I've been making sure to push my heels down low and I find that it helps keep it more stable whilst I'm riding :).