So many of us were in your shoes, trying to pull the finances and family together while simultaneously being sabotaged. However, Accepting the inevitable (acceptance is the final stage of
grieving a relationship loss) is a step forward.
Losing a house is not as great a loss as you may think. Kids don't need a particular house, annually millions of families with kids around the globe move. A house is a location, a Home is far more important. Yes, ending a marriage is difficult but neither parent should cling unrealistically onto the past, such as a house, as a symbol for stability. It isn't. Stability is in your Home, your Life.
Speak with the children in age appropriate ways. The younger they are, the simpler it can be.
Living in a calm and stable home, even if only for part of their lives, will give the children a better example of normalcy for their own future relationships. (They'll probably get married some day, wouldn't you like them to make healthy choices and not picking what they've known so far?) Staying together would mean that's the only example of home life they would have known — discord, conflict, invalidation, alienation attempts, overall craziness, etc. Over 30 years ago the book Solomon's Children - Exploding the Myths of Divorce had an interesting observation (the earliest quote I could find) on page 195 by one participant, As the saying goes, "I'd rather come from a broken home than live in one." Ponder that. Taking action will enable your lives, or at least a part of your lives going forward, to be spent be in a calm, stable environment — your home, wherever that is — away from the blaming, emotional distortions, pressuring demands and manipulations, unpredictable ever-looming rages and outright chaos. And some of the flying monkeys too.