I think MT's answer is probably enough, but the snaffle is a direct contact bit, and isn't the best for neck reining. When you neck rein with it, it puts pressure on the outside and sends a mixed message. A stiff curb (not hinged or jointed) is designed for neck reining and is not good for direct reining.
Do either of you have a suggestion then for our stud. My DIL rides him in a snaffle or a bosal. In both, if he does not wish to turn, he will go straight ahead - often with his head pulled clear around. I know - he's an appy so who knows. My DIL was thinking a baseball bat (and I think she's joking about that)