There are lots of issues here.
No one can force her to refinance unless the mortgage company agrees.
You probably have no right to the house except a possible reimbursement claim for community funds spent on it during your marriage.
She has no title to the house, just the duty to make sure payments are made.
He needs a will in any case, and may choose to leave you the house in his will. The mortgage might still be in Ex's name. You would probably have a homestead right too.
This answer DOES NOT establish an attorney-client relationship. This answer is based on the limited information provided and is not intended to be conclusive advice. There are likely other factors that might influence or change the advice after a more lengthy consultation.
You would be well advised to consult with a lawyer now to get this situation straightened out. Lots of issues here. Who is making the mortgage payments? Does the agreement or decree that gives him ownership require him to refinance?
This answer is for information purposes only, and does not establish and attorney client relationship. James Faucher is licensed to practice law in North Carolina only. You should always contact a local attorney to get location specific answers about the law.
As already stated, there are a lot of issues here. You are in a very vulnerable position as to ownership and as to being dragged in to unwanted litigation in the future. These problems will probably not soften with age. Get an attorney and deal with it soon.