Okay, the leg pressure you're describing I understand - I learned to ride that way years ago. She learned to ride western only so doubt she uses the inside leg much.
He does respond to leg pressure when he wishes to - I haven't seen her work him on sidepasses so that I don't know.
Shoulder in/out - no, that I don't understand. It seems the problem is not in his understanding her signals, it is that every once in awhile, he decides to just ignore her.
She had no problem rating him on the endurance ride, most of the time on trail he's alright, generally well behaved in the ring or exercising around barrels (she's using that to teach him to turn well) but then he just gets muley and decides that even is she insists he go right (or left) and she makes his head go that way, the rest of him is going straight.
Well, if he were pulling that on me, I'd apply hard heel far back on the inside and push his rear end around.
The shoulder in and out are exercises that work on supplenss and leg yielding, following a straight line down the arena wall with the horse canted diagonally to the track. In essence it's a trotting semi-half-pass.
I think all horses try this kind of muley "I'm not going to turn" kind of maneuver at some point. Barn sour horses, or horses being made to leave the group or whatever track they think is the right way to go.
I would do like I said above... Pull his head around and apply hard inside heel as far back as she can to push his hind end around as a corrective measure, then when he has turned, soften and do another circle around right there until he does it with the ease and suppleness you want.