She needs good manners just like any other horse. As she gets fat, you will find that more of the Thoroughbred will come out in her. I would get some real firm boundaries set now or she will be dragging you all over the place in a few weeks.
Horses look at softness and kindness that is shown at the wrong time as weakness. Timing is everything. Rewarding mistakes a horse makes with soothing and petting only teaches them to make more mistakes. Most people that try too hard to be good to one get pushed around and oftentimes hurt by the very horse they are trying to 'save'.
Even if you do not spend money on a trainer, I would suggest you 'hang around' one and volunteer to saddle and unsaddle horses, groom some, bathe and hang them out to dry, etc. We let people do that all of the time and they all tell us they learned more by 'osmosis' (by being around us and the horses) than they ever thought there was to learn.