A few things I see:
The saddle does not look like it fits you at all. You’re in a chair seat, which means you can’t use your legs for support. Even in a Western saddle, your legs should fall under you. That gives you a base of support, which you’re lacking here.
You’re very tense, and it shows. You’re riding defensively, in fact - hunched over at the shoulder. You need to sit up straight, put your shoulders back and your elbows at your sides. Hips and seatbones under you.
You need to relax into the saddle. Find the center. Get your seatbones squarely in it. You look like you’re riding on the cantle, as others have said - this could be because you’re fighting your leg position. I think you need a bigger saddle, to be honest.
Drop your stirrups altogether, let your legs relax under you, and then have someone video you riding at a walk to see how your leg position changes. See if it makes a difference to how you feel in the saddle. I’ll be you feel more secure in the seat, and start to feel your core engage more.
And I agree with the others - I’d rather see you posting the trot (once you get your saddle situation straightened out; until then, you’re going to be fighting to do it right). Have you been with this instructor long?