#1 don’t blame his past
Start with a fresh slate and remember you are dealing with a young, green thoroughbred. The idea at this stage is to take small steps and install the basics. If he masters a new concept well and easily STOP. Don’t keep loading things on him until he’s fried. Always end on a positive note.
Ensure he is free of back pain and is wearing a well-fitted saddle. No amount of padding will correct poor fit.
He needs consistent, daily, work at this stage. If you let him sit for 2 to 3 days between rides he has time to bottle up a lot of energy which expresses itself in naughtiness.
Horses will take the easy way out. Make the right thing easy and the wrong thing hard. With a TB, keeps his feet moving. No rest near the gate. When you are done riding, dismount as far away from it as possible. Make the gate = WORK.
It sounds like you and your trainer don’t have the experience to get him past this stage. That isn’t an insult… It’s why people specialize in bringing green horses along. I strongly advise you to put him in professional training with a respected trainer for at least a month, preferably one who will let you audit his training sessions and explain why they are doing what they are doing. Not only will he learn the basics, but you can learn, too.
Horses enjoy their work when they are confident in themselves and you. That confidence needs to be built in steps. First on the ground, accepting your leadership by calmly executing and submitting to your requests to move where and when you say, and then transferring that to the saddle. Bending, yielding, tempo, balance. All these things must be established before you can move on to jumping.