Go for a drink, but let this girl know that at this time, you ultimately still want things to work out with your wife and family, even though you think that things don't look so good at the moment. You go out, enjoy her company and wait to see what happens next. Can you do this without leading her on and getting emotionally attached? I don't know your whole sitch, so maybe listen to those who do, but I don't think there is anything wrong with having a drink with her.
Good luck. Wish I was in your position!! I may just run off with the new girl at this point! I see you registered in '07. Has this mess been going on for that long?