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Why should either of them get it? Sell it and put the proceeds in trust for the children. This will defray the costs of foster care or adoption. Many loving families will adopt if they can afford to do so. All this crap over who gets the house, when if these people were decent in the first place they wouldn't be subjecting their children to this crap.
However, I don't necessarily think brawling couples are more common than the truly battered.