I understand your sister wants to keep the house and continue on like nothing has changed, but she will have to "buy" your half of the house and the remaining balance on her half with a new mortgage. It's not even a simple refinance in this situation. If she doesn't have the credit to qualify for a mortgage it's not heartless to say no, it's the responsible thing to do. You could contact a mortgage broker in the area to see if she does qualify, that's usually free of charge, and that could help her realise it's not a reasonable expectation at all. This happens often, the mortgage broker should be able to handle it kindly. (it happens in divorces as well) I'm sorry this is dragging out for you, my sympathy!
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