Two things stuck out to me: 1) fingers. Your arms seem to want to do the right thing, and generally you seem to provide a soft ride, but you tend to fiddle with your fingers. Every adjustment is a nip, and that's what I saw causing your horse to toss his head. (I chalked it up to that or bugs that I couldn't see.) Also as previously stated you are turning your thumbs in, "puppy pawing" or "piano playing." Even if your arms are soft, this is still a bracing feel. Thumbs should be up, pretend that your wrists and fingers don't exist. 2) I notice particularly in the video during the canter that while your seat is good, you are lacking a connection with your stirrup, and hence way too much foot is slipping through--the heel comes up, you end up sitting on your butt, literally without a leg to stand on. I understand that you are working with a dressage trainer who most likely adheres to the longer-leg style of riding, but at least until you master the canter it might be worth asking to put them up a hole.
I also notice that a lot of reviewers are commenting on how you seemingly "lack a connection" to your horse. This may come across as a rant, but I think that sometimes on this board people feel the need to express their highest level of understanding, or the most sophisticated change that could be made for whatever reason--probably on the assumption that it would help the most. However, I think that you shouldn't concentrate on trying to find this connection. For someone at this level, I think you are doing a bang-up job, and while grasping the key ideas, you're stuck in that position of waiting for your body to catch up; to find the muscle memory, strength, reaction time, etc. That is to say, you won't find this connection until your position is solid. Keep working on your basics, and it will come. And keep riding bareback!! THAT, more than anything, will teach you to sit the trot! :o)
As for the horse, flipping adorable. Seems like a super solid citizen, willing to push you just far enough that you have to work for it, but not so hard that you would give up on him. I like him. Seems like a comfy ride too.