Neck reining

Like others, I teach neck reining in a snaffle only. They move to a shanked bit once they have a full grasp of neck reining and any other advanced maneuvers required for that horse's particular discipline. Muppetgirl did a good job explaining how, I do pretty much the same. One step at a time, simply asking for them to move that shoulder over while in motion. The forward motion is a crucial piece. Like a car, you can't just turn the wheel and get where you want to go without any gas.

With a greenie that has no concept of neck rein but does direct rein & respond to leg I try to make it one smooth motion so they can connect the dots. Outside leg asking to move off of the pressure, light neck rein and open the door on the direct side. If they need a bit more encouragement a very slight lift of the direct to "show" them what you are asking with something they already understand. The neck rein is the "ask", the leg & seat is "tell" and direct if needed is "show/remind". With consistent leg, seat & hands they will put it all together fairly quickly and will eventually work well with any of the cues together or as individual pieces.

What about a horse that overturns when neck reining and shoulders through the open rein?

With direct reining, you have lots of refinement on each individual rein being in each hand and it is easy to pick that shoulder up or close it out if the horse really dodges through it. I know you can use that inside leg to give a bump bump to keep them from falling in too fast.

Maybe a horse is a little too sensitive or spastic? Maybe my cues are too heavy or not in the right order when riding a new different horse.

I direct rein my mare and would like her to be able to do both. Is the above just the classic symptoms of a green neck reining horse?

I am guessing serpentines in the arena with lots of moving off the leg for correcting the falling in would be everyone's advice.

I would just go to the neck rein, and if she fell in or shouldered like that I'd reach down with my hand, take the rein and move her out.

Just because you have one hand doesn't mean you are confined to one. Even on my finished horse if she's had time off I will reach up and bump her over with the free hand if one hand isn't cutting it.