"for some reason and if I try to push his haunches right, he swaps leads. "
Because this is the wrong thing to do. ’
A horse cannot be straightened by trying to move the haunches ‘back where they should be’. It does not work. It throws the horse off balance. That’s why he has to swap leads.
It’s also quite possible that he simply thinks you’re cueing him for a canter on the other lead! But that points out the main problem with trying to straighten by moving the haunches, which is, it just doesn’t work.
He must have read a dressage book at some time.
Put the shoulders in front of the haunches. Don’t ever try to straighten a horse by putthing the haunches ‘back where they should be’.
Why? As one trainer told me, ‘because then there’s nothing for them to be behind!’
Think about it. The haunches are the drivers and supply the power.
Say you had a giant pillar you wanted to balance. The top is not in line with the base. What do you do, you move the top of it so it is aligned with the base. You don’t try to move the base, or the whole thing is tipping all over the place off balance. Same with a car. You have to keep the front wheels aligned exactly in front of the back wheels, or you lose power. The steering of the car allows you to keep the front wheels in front of the back wheels.
When you skid on ice, you NEVER try to steer against the skid, you turn the front wheels with the skid, so that the front wheels get back to in front of the back wheels. Without that, you have no power and no traction - with a horse, no balance and no power.
In other words, when the haunches drift to the inside, do shoulder in or later, a shoulder in like feeling, where chiefly the inside leg and outside rein encourage the horse to, like he does during shoulder in, connect well with the outside rein, and have the position of his shoulder corrected by a shoulder in like position/feeling.
Of course you don’t drift in completely off the rail, because your inside aids are telling the horse to stay on the rail.
The outside aids mostly are the ones that position the shoulders and control where the shoulders are in relation to where the haunches are. The outside aids also need to ‘draw the circle line’ in turns, circles and other work.
Of course, the outside aids can’t do that without the inside aids. One can’t straighten a horse with only one leg or one rein - all the aids work together.
Why doesn’t your work at the trot help at the canter? Maybe because you did it at the trot and not the canter?
Or because when you did it, you didn’t really get the fundamental piece of it - that it teaches the rider that it is the outside aids that control and position the shoulders. The inside aids and outside aids make what amounts to a ‘channel’ that keeps the horse straight and balanced.
Maybe because there is more impulsion at the canter, more loss of balance at the canter, and in part because of the mechanics of the canter, horses always tend to put their haunches in a little bit, and have to be specifically trained during their entire career not to; they typically put their haunches in MORE in one direction than the other at the canter, but both directions they do, and need to be trained all along to be straight at the canter.
