It sounds like the mare is responding to pain from the bit. I would first try to resolve this instead of resorting to equipment. Besides, a flash noseband is not going to keep a horse from opening it's mouth or tossing it's head, the only thing is does is keeps the bit quiet in the horse's mouth, unless you have it grossly mal-adjusted.
First thing is first, check that it is not a physical issue. Get her teeth checked, get her head neck and back examined and perform a flexion test to rule out soreness or lameness.
A few things I would try bit wise would be a double jointed snaffle, or a french link snaffle with at least a 22mm diameter. Then if that doesn't work I would try to find a suitable mullen mouth snaffle. If you are still having problems then I would go to a mullen happy mouth snaffle or a completely rubber snaffle.
The final thing I would like to add is that the rider should never pull on the horse's mouth, instead they should use weight and body langage to slow and turn the horse.