Horses are rarely stubborn, they are mixed up by what is being asked. The question is why the horse goes into a rail in the first place. And how tactful the rider is in PLANNING the use of aids/figures, and if they know how to plan the exit into the next movement as well.
The solutions to all these things are rider based, you have to ask the horse in such a way that it can say 'yes'. That might mean going back further in training to more simple actions, or having better timing, or having your teacher show you. It is NOT about dominance but CLEAR leadership.