Before I list the things I saw and what I'd do to try to fix them, let me first say, you're not that bad. You're obviously just starting to learn to jump and you're not real stable at it YET. Yet is the word to remember because you will keep improving.
1st, I'm not really seeing that much of a chair seat but it looks like you're alternating gripping with your knees, then your calves and back to the knees again. No thigh involvement in there at all. When you come up to the jump you're throwing away your reins, I suspect because you don't want to bang him in the mouth. That's a good thing to not bang his mouth but throwing the reins away in front of the jump is like if you and I were walking along on top of a wall and I was holding your shoulders to keep you steady and right before you stepped across a gap in the bricks I kind of gave you a little push at the shoulders and then pulled my hands away. He kind of drops on his forehand and wonders where you went.
The little bit of cantering I saw you were bracing against the stirrups with your legs, butt and hips real tight and no give. First thing I'd do is either start wearing a tall boot or a pair of half chaps in the lesson. They'll help you hold steady and not feel like your leg is swinging all over the place.
When I was where you are in training, I did cavaletti for hours, and my trainer had me work a grid, with and without stirrups. Trotting and cantering without stirrups for hours and hours was another exercise to develop the seat. She also would put cavaletti in front of and after the jumps and it was my job to hold the horse steady and not let him break from the trot. If you need help balancing bridge your reins on the crest of his neck before you get to the jump, or grab mane with one hand until you get the timing down. Those jumps are small enough that you don't need a big break and crest release, you should just trot up in 2 point and flow over with the horse. Instead of posting up to the jump, maybe go into 2 point as soon as you make the turn toward the jump, get settled and comfortable and by the time you get to the jump it will be no big deal.