Any possibility of letting the current GM fall on her face and then getting promoted into the position?
Maybe it's an opportunity, not a problem.
If so, although it's got risks, you can work to set that up by going to whoever has the power to hire and fire GM's, letting them know the problem (documented in detail), that you would love to take over the position, and that you'd do an excellent job for them in that position, helping them make more money than if they keep the current GM. The risk is if the GM hears of it and has the ability to make your life miserable. If they don't flat our refuse, but seem hesitant, you could sweeten the pot -- offer to do it for less than she does, or do it for 3 months at your current salary, and if they don't like the job you are doing, move you back to your current position.
Good books to read to help you negotiate things and convince people:
How to Win Friends and Influence People, by Carnegie
You Can Negotiate Anything, by Cohen
How to Make People Like you in 90 Seconds or Less, by Boothman