The fact that your mare doesn't let you take a feel of her mouth makes it difficult to work on her issues with straightness. She should not be evading your hands by getting quick when you put pressure on her. I would say start off on a circle first going in the direction she likes and with a softer rein asking her to flex and soften her mouth to the right and left with steady leg keeping in a nice working trot. Its hard to get too strung out on a circle to so that should help and you can do a walk transition if you need to. Then, when she feels like she is yielding nicely you can try the same in the other more difficult direction. Also, doing this and mixing in upward and downward transitions should keep her attentive and engaged.Hope it helps. Good Luck!