Firstly, look at what the horse is thinking when you go to mount. Taking off in a straight line tells me that she is impatient and not respecting you or she is running from pain. So the first thing that you have to do is to check the saddle out and see if its causing any pain. With that out of the way, you must change the horse's thinking. You can't pull on both the reins at one time, ever. That just gives her a barrier to fight against. To use treats would just teach her to look for that instead of listening to you. The act of mounting is always an "iffy" in terms of your safety and should be done safely. Standing her in a corner is just another barrier...what if you were out on the trail and stuck in a bad position where taking off forward was just not an option? Bottom line, you do not have control and you are not safe. You have also reinforced this by getting on anyway even though she is moving forward. (sorry, truth hurts, doesn't it?)
You'll have to give her some mounting lessons to get her straightened out. I would go to an enclosure of some kind and let her work the kinks out to the point where she still has energy, but is not doggy. The enclosure will help to get her to realize that she is not going anywhere. After the kinks are out, I would saddle and bridle her slowly and look for anything that may be causing her pain. You should have one wrinkle in the corner of her mouth for proper bit position. If you have a curb strap, you should be able to get two fingers under it when there is no tension on the reins. (I would use a snaffle bit for this lesson, though) The saddle pad should be clean of debris and have good loft. If its well used, it will have pressure memory and checking out the shape of it will sometimes tell you where the pressure is happening. You should be able to stick 3 fingers vertically under the front of the saddle where it sits above the withers. The channel down the spine should also be up and off the spine. When you are sitting in the saddle, there should still be two to three fingers above the withers. When you sit the saddle on the horse's back, run your hand under the saddle from front to back on both sides and see if anything is digging into your hand. If there is, its going to dig twice as bad when you put your weight in the saddle. Make sure that the girth is clean and that the skin is not pinching when you do it up and do it up in increments, walking in small circles, then doing it up a little tighter each time. Not only will this prevent the horse puffing up on you, but its better for the horse mentally to adjust to it as well as physically, because the girth lays over a main artery to the heart as well. Put lots of bug spray on before you start, if necessary and expect the horse to stand still for this lesson.
You start by standing on one side, at the horse's shoulder and facing front. Put a little pressure on the rein on that side, just enough to get the horse thinking about it...and wait, wait. The horse will try to avoid by moving, raising her head and doing different things to relieve the pressure. Move with her, whatever you need to do, but keep the pressure on until she does the right thing....turning her head toward you, instant release, lots of praise. Do it again. It should take about 10 minutes for the horse to figure out to give to the pressure. She'll get the hang of it, do it well, then get doggy about it, but persist and reward when she does it. Once she gets over the doggy part and is responding again, that's when she's really learned it. Then do the other side. Once that lesson is learned, then putting on pressure, her giving, continuing to hold pressure instead of releasing like you have been and she'll start moving her back feet away from you. That's disengaging her hip and the only way that you can truly stop her. This is called the one rein stop and is essential for your safety in all situations. When you get to the mounting, lengthen the stirrup on that side to make it a little easier for you and the repetition that you need to do. Tell her ho and move slowly back to the stirrup area, ask her for a give, release, praise. Feet are not to move at all during this exercise. Shake the stirrup, ask for a give, release, reward, make her smell the stirrup and move it around, snapping the strap and increasing the intensity to increase the desensitization factor....weight on stirrup, foot in stirrup, hopping while foot is in stirrup (put the ball of your foot where it needs to be in the stirrup and watch your toe) Lifting yourself to a standing position in the stirrup on one side, then swinging your leg over, settling and still she must not move till your say so. Everything in small graduations, give, release, reward. Ask for a give everytime you see her tense, raise her head and is about to move. Have her in a give position when you mount. She is looking at you, is listening to YOU, has her hip disengaged and has nowhere to go except around and around. If she's smart, she'll have this fact down pretty fast. You've got to do the other side too, every step of the way and it's a lot harder, cause you're teaching yourself to be ambidextrous as well, just mirror your movements from the good side. Well, are you up to it? You asked, I answered, and sorry, I did go on with this one! I think you have a wonderful trail horse that has the heart of an endurance horse. She's looking down the trail, she wants to go there. I think that's wonderful! Sure a lot better than a horse that is constantly thinking, "o.k., now, I'm leaving the barn, leaving the barn, LEAVING THE BARN! LOLOL! She just needs to learn to be polite and safe about it. Hope this helps, happy trails!