Two things;
1. Lay it all on the table (figuratively) with her mom first. Tell her you are game but that you need assurance that she is going to keep it totally discreet and no matter what, it would be something she would take to the grave. Tell her you need to know that she'll have no sudden attacks of conscience and suddenly have a 'need' to tell her daughter what happened. Then tell her that whether it happens once or a thousand times, when you say its over, its over and that there will be no hard feelings, revenge, or jealousy from her.
2. Hit that shit like the boss you are.
Seriously man, this is my all time #1 fantasy. I have wanted to bang my MIL for almost 10 years and have never had the balls to make a move because I have no idea how she would react (in fact I just made my own confession earlier today regarding this).
You however, have no questions about her intentions, have a total green light, and yet still are hesitating? Don't get me wrong in a way I admire your fidelity to your woman. I love my wife more than anything and see her in the same way you described your gf and so I get that you don't want to hurt her. However, you are in a position that thousands of men have dreamed of finding themselves in. The difference is most of us never get past the fantasy.
My advice? For whatever reason, the universe has decided to throw you a bone my friend and I suggest you reach out and take it after a good heart-to-heart about the rules with your gf's mom. Good luck and keep us updated.
