At the walk and the canter your horse uses his head quite a bit to balance himself, so it's going to be moving rythmically up and down. At the trot, he can keep his head in one spot while moving his legs in their respective pairs.
For some reason, you are saying that it's harder for you to keep your hands still during the gait when your horse's head moves the least. Perhaps, during the trot and canter you are more actively following the head with your hand, but during the trot your hand has nothing to follow, so it ends up following YOU as you are posting.
Does that sound like something you are doing? I mean, as you post is your hand affected by your up and down movemetn so that it , too, is going up and down?
One thing that I have tried is using a piece of string or leather attached to the D ring of your saddle. About 10 inches long. You put the string in one hand, postition your hand vertically where it should be and set the string at a length where there is no longer any slack when your hand is at the height it should be. Start trotting, posting and don't pull too hard on the string, nor let slack into the string. It will help keep your hand in the correct position. The hand without a string can just follow the hand with a string. This will help you learn the feeling that you must have in your ELBOWS . It is your elbows that will bend and open, bend and open with each stride so that your hand can stay in exactly the same place relative to the saddle/horse.
Practice posting without holdig the reins at all, like on a lunge line, will help you learn how to post without using the reins AT ALL to help keep your balance.