Okay, please don't take this the wrong way, as it is not meant to be an insult of any kind.
It seems to me that your horse is trying to get away from you, as in she doesn't feel safe with you. Something that is happening, or something that has happened in the past, has made her feel unsafe. She runs to other horses becasue in her mind, that is where the safety and comfort are, not with you.
Take this one step at a time. First, you need to make her feel safe. When you mount up, walk her around on a loose rein and just rub her neck. Take a "passneger lesson." Basically all you do is tell her "You can go anywhere you want to as long as you stay in the walk" for instance. You do NOTHING. You are simply a passenger, not a driver. The purpose of this is to let your horse know that you can go where she goes, turn when she turns, etc. and be in harmony with her and not restrict her in any way. It's also a really good time to focus on how she moves, what it feels like when she stops, turns, etc. Here is the cool thing about this! If she goes to that corner ALLOW HER TO. Don't try to stop it. When she gets there and stops, rub her, stand a moment, then ask her to go again. This is not rewarding "bad behavior" it's simply letting her know that everything is okay and that she has nothing to worry about. Soon, if you are consistant with this for many sessions, she will start to think "Why did I want to go over there so bad anyway?" When you become just a passenger, the horse calms down, gets softer, etc because again, there is no fight and no restriction. It's reverse psychology. If you do this, it will really start to feel good to her, so she won't feel the need to race into the corner because riding isn't so bad after all. Slowly, you can start to take over again and start "driving" again.
One thing I should mention is that if she breaks gait at any time, like goes into a trot or faster then what you want, use one rein to slow her down. When she is good at the walk, try the trot, then eventually the canter, but don't be in a hurry. Take your time. Invest this time into your relationship with her. Also, if she stops at any time, allow it. Rub her, wait a moment, then ask her on again. Do what she does. Mirror her movements. If she looks left, you look left. If she turns, you turn. If she sticks her ribs out to one side, you do the same thing in your body. This is all about getting into harmony with your horse, and once she feels this, she will calm down because you will start to feel like one unit instead of 2 oppossing forces.