Wow. Ok, your problems are not religious in nature. Counseling seems important. My question about the children was that if you married in the Orthodox faith they would require you to agree to let the children be Orthodox. Seems like you don’t care, so that shouldn’t be a problem.
I guess the best advice then is to talk to an Orthodox pries with your wife. Perhaps she will listen to him, and see the importance of having the marriage regularized. I mean, if the orthodox faith is important enough to her to want to convert you, I’d think she’d be willing to listen to a priest.
If not, and if she is just being spiteful, I’d certainly have no interest in having marital relations anyway…anyone that spiteful would not be arousing those feelings in me.