Great critique from pepperduck.
I just want to tweak something she said
Loosening up your arms won't stop your hands from moving. Posting is just moving your hips forward and back, that's it. You are currently posting with your upper body/shoulders, causing your hands to move around. Really focus on moving your hips. With a correct post, your shoulder doesn't go up at all.
Since I suck at explaining, heres a pretty good example of what I was talking about
It's really important to keep your hands steady, especially on a green horse