Do please bear in mind that grief at a loss does affect different people in different ways. I lost my parents five years ago and it's only now that I feel able to deal with their assets. Could it be that, having lived with your father, she's finding it difficult coming to terms with the situation?
In our case, I bought my sister's share of the property at a discount and have paid a mortgage ever since. Would you be prepared to make an offer of this kind to your sister? And, of course, does she have the income to pay the mortgage?
I really hope you're able to sort this out, it's never easy.
Good luck.