To teach the one rein stop, saddle up in an enclosed arena or paddock where you are comfortable riding. Not too big, you want to feel comfortable completely dropping contact. If you have English reins, with the buckle in the middle, hold the buckle with one hand and ask your horse to move off at the walk. Don't steer, just let her walk. After you have gone about, oh, 8 strides, take your free hand and run it down the length of that rein, reaching about halfway to the bit. Grip the rein and pull her nose around to the girth. When you pull the rein, bring your hand up to the point where the seam of your jeans meets your belt. No higher, or she could off-balance and potentially flip over. Hold this position until she
gives and lets the slack out of the rein. (It doesn't hurt to flex her neck like this from the standstill either
) Flex the other way, to keep her muscles moving evenly, then move off at the walk again. Repeat. The next time, pull her to a stop with the other hand, again to keep her from getting one-sided. When she stops off of one rein softly and instantly in both directions at the walk, you can progress to the trot, and on to the canter after you are proficient at the trot. Over the course of teaching, whenever your horse moves faster than you want (trots when you want a walk, for example), do a one rein stop and flex her, then ask for the gait you want. I hope that's clear enough. Clinton Anderson's is the method I've just outlined, and he has much more in depth instructions in his books and DVDs.
rides in the twisted wire snaffle??!! It doesn't sound like she feels that she has the "strength or ability" to stop your horse, and she is the trainer!! Give the milder bit a try. If you ride in a halter, and the trainer rides in the twisted snaffle, then she may not be as soft in the beginning, since she's used to a harsher bit. Do the one rein stops in the new bit and she'll get softer and lighter. Ride her as often as possible in the new bit, and ask your trainer to ride with it as well, as the horse should be trained in the bit she will be ridden in by the owner. It just doesn't make sense for the trainer to ride in a harsher bit, and then have the horse go back to the primary rider and a milder bit. Does she ride all of her training projects in the twisted wire bit? Maybe she has a third cousin who makes them, lol. Nearly any horse can go in a plain snaffle and be stopped, it just takes a little time and patience.