I agree with Speed Racer, entirely.
I too recently acquired a ten year old OTTB mare.. she was on the track until she was seven and used as a broodmare for a couple years until she was started under saddle. My instructor and I don't believe that was never truly given any boundaries, so I've had to be consistent all the way through. She also would back up on me, whether I was getting on and at times, when I was trying to get her to go forward. Whenever she pulled something on me, I'd pull something on her.. and as a result of that, she's finally starting to respect me more.
About the trotting off, just spend all your riding time on fixing that issue. Indie would try trotting off after a few steps at a walk, so I spent a good couple hour long sessions just at the walk. I'd keep her on a loose-rein, but as soon as I felt her starting to trot, I'd pull back. Eventually, she went from one circle on a loose-rein to a few laps on a loose-rein. Also, practice getting her to stand still.. start with five seconds, and gradually increase it, then give her a nice neck rub if she stays still.. if she starts prancing, wait another five seconds, etc. It might get boring, but it'll pay off in the long run.
Forever loved, never forgotten; my beautiful Indie. <3 Hoofprints on my heart.