I just bought a ten-year old mare. When we went to bring her home, we rode her and she was an awesome horse that can turn on a dime and had power brakes. We got her home and she keeps shaking her head when you try to stop her. Sometimes she will stop perfectly though. We tried different techniques, from a hackamore to just using a bridle and lead rope as reins. Nothing works. Could this just be nervousness from new owners and new surroundings and if so how long does it usually take for a horse to calm down?
Start by asking the previous owners what kind of bit they rode her with. How they went about things with their training sessions and exercise, and this might answer all of your questions. If she is throwing her head it sounds like too much bit. It is hard for me to guess what might be the problem without actually seeing what is happening. Start with researching the past history.