Another thing you can try is to have your friend trot just 3 steps and then bring your horse back down to a walk, trot 3 steps, then make the horse walk again, and just keep doing that until your friend is comfortable, relaxed, and controlled doing it. That will help with both her seat and keeping the horse under control. Once she can do that, then you can start upping the number of steps the horse trots before going back to the walk. Trot 4 steps, walk, trot 5 steps, walk, etc. I've taught some very timid beginners to trot that way, and it really helped them!