Squirrel, I am so sorry to hear that all this ->-bleeped-<-e is going on. It sounds to be a very complex situation. It also sounds as though it could go either way. Agreeing with Cindy, the best case scenario is that you effectively become your partner's therapist and help him express himself and lose his shame at his cross-dressing. The result could be a relationship that is closer and more full of mutual understanding than most couples experience. The worst case scenario is that he continues to reject himself and so you. You remain at loggerheads, he continues to be passively agressive (the money thing, the position he has given himself of martyr and blaming YOU for the stress caused by his inability to adapt) and both feeling betrayed and misunderstood.
It must be indescribably difficult for a partner to accept their SO transitioning. I would like to think that I would stand by mine if he chose to, but who knows? I love him as a man. Could I adjust my sexual orientation to love him as a woman, or would I constantly hanker over what he used to look like? My partner believes that he could not remain as a sexual partner if I transitioned. And, because it would break my heart to lose him and tear up the family, I am not looking at medical treatment for the foreseeable future. But, the thing is, your partner is staying with you but kvetching about what you are doing. He needs to make his mind up. Get out or grow up.
But, as you say, the bottom line is the happiness of the kids. And they can't be happy if you and he are obviously not. A calm home with a single parent is better than one where the parents are constantly battling.
I really feel for you and wish you all the fortitude you will need to sort this out.