I can't imagine that the atmosphere in the house is very good right now. Is she staying out of spite or does she have no place to go? If you bought her out (Just making a guess, if you've been making payements for a year, plus a down payment, your buy-out offer, even at 20% is probably at least a few thousand dollars) would she be able to get into a place of her own?
As long as the 80/20 split is in a contract some where you may have a leg to stand on legally, otherwise you may need 50% to buy her out, and that could screw you.
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