Dude, you are going to run out of feet to shoot yourself in. I can just imagine you telling her off about the divorce. Any F words flying?
You need a cooooooooooooooooooool head. That is why you have to detach. I get the impression that you use any interaction with your W to show her what a dick you can be.
Do not get into debates with her, esp. not heated ones. You need a cool head on your shoulders. Just politely say to her, that you hear her request, but you do not believe in divorce.
I am not familiar wit the laws in your state but, usually you can go the distance without the lawyers too much involved if both parties agree on the most important bits (children, spousal support, alimony and division of property). DO GET PERTINENT LEGAL INFORMATION ASAP, ESP. WITH REGARDS TO YOUR DAUGHTERS.
Don't be a dick, but do not let her railroad you either.