hmmm, interesting, Volker. video of this side to side discrepancy?
I know from watching myself - I don't always match my body position/action from left to right. For example in circle work (longeing - like)- I tend to be much more forward (relative to the middle of the horse) going to the right. I also turn my body in different ways - I tend to face the horse more from his right side... So I would suggest reviewing your cues, doing them slow motion away from the horse - just imagine him there. You may be able to figure out the difference by moving your imaginary horse from your right to your left
Unless, of course, your School Halts involve bend or flexion? - that could affect the horse...