Nice horse, crappy video (gave me a headache just looking at it so had to start/stop it several times to be able to evaluate your riding).
What I saw:
1.) Your seat needs work. You lean forward and pull your knees up at all 3 gaits. Then you use your heel to get upward transitions - you are supposed to use your calf. Using the heel ensures that you will continue to pull up your legs (it's not just the heel rising, sometimes it's slight, other times your entire leg is out of position - it's a wonder you stay on!).
2.) The connection to the horse needs work. Your elbows should be on your waist UNLESS you need to give - and your entire body need to follw the horses movement. Especially at the walk the horse will "bob" it's head up and down - you arms need to follow (back and forward) appropriately. When you fix this the horse will stop "shaking" her head.
3.) Several times when I stopped the video (more towards middle of ride) I noticed your legs are too far back (WELL behind girth, not just back to retain canter lead or turn).
4.) Look where you are goiing, not on the ground. That means looking forward (or if you need to look at horses head/neck position ONLY use your eyes).
5.) Lift ribcage (REALLY helps in upward transitions) and engage your core (stomach muscles).
6.) Front of horse moves nicely, back end didn't "track up" until around 1:14 in the video. That means horse is probably behind your leg and you probably got comments on needs more impulsion. Horse was using back nicely (evidenced by the wagging tail).
7.) In a few spots horse was tilting head (nose to inside, ears to outside) - fix contact and that will probably fix itself.
8.) Corners - when you turn a corner take your inside hip forward and use the ouside rein (squeeze/soften) and leg (no push just blocking to prevent horse from throwing haunches to the outside) to turn.
Other non-riding things I noticed:
- Pocket was out of jacket
- Hair was messy and hanging out of cap - get a hairnet
- You need a longer whip - you's is short so to use it effectively you'd really have to move your arms out of position
- Around 3:11 horse "fell" into canter and looked like she gave a small buck?
You'll get there - some sort of feedback (like a good video/mirror/...) will help you get there sooner. Good luck.