I think with strong horses, you just have to learn to go with their pace and not fight them every step of the way. Some horses hate being micromanaged and like going fast so they resist you every step of the way and come off as 'strong'. Also using a milder bit might help and giving and taking with the reins and doing half halts.
I have the same thing with my horse, so I use a rubber snaffle
I also have a very strong horse the thing that really helps me is to use a softer bit. As well has opening and closing your hands when you ride. I usually open and close my hands on the reins with the motion of the gate. It also helps to close your leg to push her head into the bridle. Hope this helps.