We are separated while living together for the sake of the kids. Can this possibly work?

After 12 years of marriage and 3 great kids, my marriage is falling apart. My wife has been living in a separate room for 9 months, and since then things have just got worse. There is no infidelity involved, she just doesn't feel the same about me any more. She unfortunately suffered childhood abuse over many years, and the result of much counseling seems to be that i as her partner has been identified me as an abuser too (which I have NEVER done). This seems to be triggered through any attempts at me initiating intimacy on any level (even a simple kiss!). She gets very defensive about the abuse being the problem - and there are every day things that annoy us both as per any marriage, but the abuse is an important core reason. I have apologized over and over again if my actions have made her uncomfortable, and explained that i want this to work, but she has been keeping her feelings bottled up for a long time. She is now very clear that she regards us as officially separated. We seem to be at a stalemate as to what to do next. I am the sole income earner in our family, so I can't afford to just move out and rent a place of my own, and in any case I don't want to leave the kids; I don't want them to ever think that dad just walked out on them. So we are living at separate ends of the house, and going from complete silence or arguing if we talk about real things. i am mild mannered by nature, but she gets so aggressive that I am at my wits end wondering how we can go on living like this. And what really sucks is that this is my 2nd marriage - you think I would have learned the first time (married my first girlfriend who had an affair - great). She acts surprised when I mention divorce as the next step, but that's where I see this going at the current rate of progress. What to do????????