It's very important to keep the shoulder blocked. Have enough contact to keep him from walking off, and your reins on his neck to keep his shoulder from popping out like that. If you have to, you could put him facing the fence for a little while.
I also second the dressage whip. If he doesn't move his butt but moves everything else, give him a tap. Release and pet him as soon as you get a good pivot from him, and relax. Just let him know it's no big deal, and he can chill through it when he does it right.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.