You gave her half the house so half the equity is hers. She has just as much right to be there as you. It was your choice to give it to her. This is the result.
Very unfortunate, but it happens every day. If there is no mortgage, you'll have to share the equity with her.
Is there a mortgage? If so, I assume she's also not on the note so you're the only one who's credit is screwed if you quit paying the mortgage. Perhaps you could arrange a "friendly foreclosure" with the mortgage company, they would own the house a short time, evict her, then sell it back to you. Your credit will take a hit but you could be back in control of 100% of the property. See a lawyer. Good luck.
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You will probably have to file a partition action. You will need to retain a real estate litigation attorney in your area. As previously noted, she is now a owner of the property, so you cannot simply kick her out of the house.
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