@tinyliny : what I'm guessing is that the horse's owner wants the horse to be ridden by another rider that's barely 100 pounds and maybe not strong enough to control the horse, so Girl girly is quite a bit worried that it will have a negative effect on both the horse and new rider. (@Girl girly did I get it?
Yes, try doing basic dressage patterns to keep her mind working. Try not to ride her around and around sticking to the arena fence. That will just be very boring for your mount and may make her stressed out. I had almost the exact same problem with my Haflinger! Still have it, sometimes. What got her to slow down was just varying the activities. Do you have trails or safe roads around where your property is? Take a friend or invite someone from the barn out for a short ride and see if she still trots fast outside the arena.
Also, the pressures in the arena may make some horses act differently. At my old barn the big indoor made it horrible to ride my pony because she would just run through me and it got dangerous. I recently went back for a show and schooling was in the indoor: outdoor for morning schooling went great, show started, I took her to the indoor before my class and she was doing the same thing she did the year before. But outside? Perfectly fine. Your mare could be claustrophobic or feel threatened in the big arena.
Make her mentally sound! ;)
For getting her in shape: walk her up and down hills. Then trot her up the hill and walk her down. Get creative! Have a game day and invite some barn friends!