A lot of that is urban legend. Courts don’t want quarreling spouses, particularly with children, to remain living together and therefore do not financially punish people for doing so. It may indicate that she is the one who should remain in the house long-term, but Gordie has said many times he does not want the house. Gordie indicates above that his lawyer blesses him leaving. He will still be entitled to his equity position, whatever that is.
You may want to consider an ultimatum here since you are willing to carry it through. Such as, sign the docs by Friday or I move forward with the divorce/move-out ASAP, whatever.
I’d weigh your mental health and the older kids’ awareness of what is going on vs how much worse you think it will get as the holidays near. At the end of the day, the kids needn’t one sane, well-functioning parent.