My instructor is basically just trying to get me to practise putting him on the bit, and giving some rein when he's being nice with his head. And if he moves out of that nice position, to put a bit of pressure on the reins, to try and get him to accept it more. She is teaching me, not him.
You do NOT ride the horse's head. You ride the hindquarter. You let the horse seek the contact.
Again, I can't even begin to tell you what you should be doing because you don't have any of the basics. You aren't being taught correctly and you aren't being educated on equine biomechanics.
Look for a new place to take lessons.