I have been in the exact same position. Keep trying. I know how hard it is re learning to position your body, but the harder you work at it, the faster the rewards will come. If you are having trouble with leg strength then go to the gym and get prepared to be sore for a while. For your pulling problem, as dorky as you look, put a bucking strap on your saddle and use it! As for the balance thing, this is a trick that was basically the key for me: balance your head. If you lean forward, then your head falls off, if you lean right, your head falls off, basically if you aren't completely centered in the saddle, every stride, you no longer have a head because it wasn't balanced on top of your body so it fell off. The more you focus on your balance and keeping your hands still, the easier riding will become.
Also: if this trainer isn't motivating you and teaching you what you want, then switch. There are plenty of trainers. And never give up. If you can't find a coach that will help you, then get someone to videotape you riding, and sit at home and watch it and make a detailed list of things you want to improve and then fix them. Your horse will also help you. When you feel good to them, they go better. And if you feel good to them chances are your doing something right.