I just watched your trot and canter videos that followed the short jumping clip on YouTube. Let me start by saying Iām not a professional. But a few things caught my eye.
It looks like this horse wants to pull like a freight train on his forehand, stiffen his jaw and invert when you ask him to balance, and leave a trailing hind end that isnāt engaged. I would start by doing tons of lateral work with almost constant changes of direction every half dozen strides or so when heās not being soft and round. This should help engage the hind end and soften him if done in a manner which wraps him around your leg and keeps him forward into an elastic hand.
Speaking of hands, you really need to work on developing and independent seat and hands (not saying this to be mean). Shorten your reins and donāt ride with your hands in your lap, but keep your hands soft and your arms elastic. When he goes to stiffen, invert and get quick on his forehand, stretch tall and ride from your leg into a closed (but not hard and pulling) hand, with a little leg yield to the outside. The moment he softens, soften your hand but keep quiet, elastic contact. Do not seesaw his mouth left and right with your hands, as this will only create more tension and perhaps an āartificalā softening where he drops his head but is behind your legs and hands and not actually engaged with his hind end.
With a horse like this, always focus on riding the hind end up to the front end with elasticity. But when he tries to invert, get quick and lug, close the leg and ride him up into a closed, but not hard or pulling, hand, that softens but maintains contact the moment he softens. The last thing you want to do with a horse like this is to get into a tug of war with him.