He is not lucid. Is there a way for my mother (they are married) to get durable power of attorney over him or is there another option? She is looking to refinance her home at a lower interest rate so that she can afford to stay there after he passes.
Unfortunately as your father is not lucid, he cannot sign a Power of Attorney. Your mom would have to get a guardianship over him through the Court. This all takes time and expense and the Court would have to consent to refinancing the house.
After your dad passes your mom should be able to negotiate with the bank for a better interest rate, so long as she can satisfy the banks requirements.
