My Tennessee Walking Horse was exactly like that. Teach him to disengage by:
Using split reins and a snaffle bit
Drawing very slowly with whichever way you want them to disengage (draw with your left, their hind end moves to the right and vice versa)
Make sure you draw and don't pull, and keep your hand just in front of the saddle horn, don't let them slide down your horse's neck. The hand that you are not drawing from should stay low and not come up when you're drawing. Very important: while you are drawing, (let's say you're disengaging to the left) turn your head to the right and look at her hindquarters but keep yourself upright and don't lean (like you have a string that is holding you up from your head). She should give to the slack with her face and step over with her hindquarters. Release when she does both and praise her for even the slightest effort. Start out with only doing one side at a time, once she get good at doing both sides, you can switch from side to side. I hope this helps you (It REALLY helped me)
You can also use the Porcupine Game on the ground. That helps prepare them for disengaging.
Sorry if I didn't explain things clearly, I'm not very good at that