I know you aren't interested in hearing this, but if I were you, I'd still be interested in why Kelly isn't responding to you. When does she act up? What are you asking for when she refuses to listen? When you identify that, ask yourself if you're giving your horse the correct aids. If you're not sure, ask your instructor. If you are giving correct aids and Kelly is still refusing to move, there is a hole in her training or another underlying issue. If you aren't giving the correct aids, how can you fix them?
Even if you do end up continuing to ride the horse your friend was already riding, you should take this opportunity to better yourself as a rider.
I have learned that if a horse is acting up, chances are, it's the rider's fault. If it's not the rider's fault, then it's a training gap, and that horse doesn't need to be used for beginner lessons.