I agree that the stopping issue is a training issue. It starts out simple, a slightly faster walk one the way home, first time out, then if she gets away with it, she starts going faster, and further out and then she starts trying to go home as soon as you take her out. I cannot stress enough how important having good ground manners is. No matter how sweet the horse may be, if it doesn't listen to you perfectly on the ground, its not going to listen to you when you are on it. Even if you ride western, don't put a harsher bit in her mouth. Start with ground manners first. Some horses do need a stronger bit, my dad's horse being one, only because he spent some 20 odd years barrel racing in a gag hackamore, so he ended up having a really hard mouth by the time we got him. I still rode him in a nice simple snaffle, but if he saw a barrel, he would try to take off and it required a one rein stop to get him to halt, and turning him away from the barrel, but then he'd listen. So for him sometimes we used something a little stronger to make sure my younger brother could stop him when he did gymkanas on him. Do lots of in hand work, and get her to listen both on the lunge line, and while leading, and only when she is listening perfectly, stopping at your shoulder when you stop, turning when you turn, ect., without any prompting, then you can get on and try her undersaddle. If she's bad enough, when you are on her, you might even try having someone lunge her when you are on her the first couple of times, to make sure she gets it right, and starts listening to you, but that way you are safe if she tries something when you first get back on.