Ok, very brave of you for posting a vid! I can hardly watch myself!!! Haha!
There was two things that really stood out to me:
1. Your feet are driven way home in your stirrups, I noticed you wriggling one out during the vid. Try to keep the ball of your foot in the stirrup....no more. Why? Because now that the ball of your foot is in the right place you can push that heel down, which in turn will seat you better. I could see during the vid that there were instances of your leg sitting well with that heel down. And at other times you were tipping forward because your foot was driven into the stirrup so your heel popped up and tipped you forward.....creating a balance issue.....
2. Balance. Your balance is a little on and off (stirrup heel issue fixed, will help immensely) I have been exactly where you are! The horse is green for sure. However I think you could really help her balance and your own balance out quite a bit by, slowing down. Everything looked too fast, loose and jarring. Slow every stride down and focus on developing some more softness and slowness. It will make everything so much easier for you to think about while riding.
I couldn't see your saddle position too clearly, but just check its not sitting too far forward.....
I think your mare is getting a little antsy because it's hard for her to do all your asking and maintain some balance....it's hard work for her.
Jogging slow circles and spiraling down to the middle and back out a again really helps with balance, for yourself and your horse.
All the best