Well in that case, I would certainly work on your hands and see if that helps. As you can imagine, being jerked in mouth constantly while you're trying to concentrate is going to get old very quickly for a horse. Teeth grinding a very common sign of this - you see it in a s lot of dressage tests, when the rider is either bracing against the bridle, see-sawing on the bit, or if their is tension somewhere in their body that is blocking the horse.
Are you able to get some lessons on the lunge on a nice quiet school horse? I am a huge believer that every rider should be able to ride without reins and stirrups at least on the lunge. This teaches you to rely purely on your seat for balance, and once you take your reins back, you won't feel the need to grab at them and jerk. In canter, you can rest your hands at the top of the wither and simply allow the hands to move with the movement of the topline as it stretches and contracts.