I can see only the first video, and it's short, so I have very little to make any kind of judgement by.
I disagree with the above poster regarding your seat. I am sorry to say, but I feel that your seat is at the place where a lot more flat work would be my recommendation, were I your trainer. Sounds kind of harsh, I know.
it looks to me that you are riding too much by a grip with your knee, which brings your lower leg off the horse, and makes your butt come out of the saddle in the canter. The stiffness in the grip makes you pop up and down when the horse canters, bopping his back and making him hollow out. I think you'd be best to sit down into the canter when you are trying to settle him, instead of bracing into te stirrup, and balancing on the reins, like after the first jump.
the horse's changes in speed and energy make it hard for you get into sync with him, that is why it is best if you can get more energy at the trot, so you are closer to the energy of the canter that the horse needs to pick up out of the jump.
These observations come from someone who does not jump, so I cannot offer specific advice on how to correct that, since I don't ride in jump saddle, and the balance is a bit different. hopefully, some jumpers can give you better ideas on what specifically to work on.