Tell your kid what she is doing. It is the ultimate win. They will be upset at first, but she loses forever. If the house is yours dump all her shit outside. If not just leave and don't come back when she is gone on her excursion. Don't answer any calls, don't talk to her, don't reply to any letters or mail (unless legally necessary). Do all the legal stuff by the book. Ask your kid who they want to stay with.
Cheats never change. Never.
Not sure getting the kid directly involved is the best idea. I have friends whose parents played the game of tearing down the other parent and bribing the child and it seemed like it only had adverse effects on the childs development. My suggesting for that is to leave the kid out of it as much as possible (Not sure how old he is so understanding at this point might not even be an issue).