Ok I think there is a bit of a communication error going on here.
First thing first, leg lield is NOT a lateral movement. It is a basic "please move off of my leg" command in which we are not asking explicitly for bend through out the body, the horses for and hind legs are moving in a similar matter.
Secondly a "leg yield down the wall" consists of pushing the horse's haunches off the track, with out bend (IE not a travers).
The reason we do this exercise this way is because it is hard. Doing a leg yeild going outwards is easy, doing a leg yield with the haunches coming into the arena is hard because it is developing the outside aids.
First of all I would work on leg yielding from the wall to the quarter line to get the horse "unstuck" from the wall. Once this is good, then I would go to the walk, flex slightly to the outside and push the haunches over using the outside rein and leg, while opening the inside leg to help position the horse in the correct manner. The inside rein acts to keep the shoulders on the wall. Once you have the positioning right in the walk, then move into the trot.
ETA about your body position it is hard to say what is the right correction without seeing a picture. Ideally we want to be in teh center of the horse with level hips and shoulders and the head pointing straight forward. Because every person contorts themselves differently it is hard to say what the right "correction" is, but if you look at a picture of yourself from the back your ears, shoulders and hips should be level and pointing in the same direction as the horse.
They say money doesn't buy happiness -- well happiness doesn't buy horses!