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.
Question on your post to cowboy on neck reining.
Is the bit used at all in neck reining. I don't know for sure, but I didn't think it was. I thought neck reining was useing the reins on their neck. That the solid bit was for one handed stops.
Becky