Can my father sign a POA over to me, his son, to handle his part of my grandmother's estate?

No. Your dad cannot do that. He CANNOT assign his duties to someone else. Only an executor can sign documents and take actions on behalf of the estate.

There r POAs for specific reasons. I gave POA to my Mom when she took my then 12 yr old daughter to England. It gave her the right to handle decisions for my daughter in case of an emergency. I can't see why Dad can't assign you POA for handling the estate only. Or like Margaret said, give up his executorship. It really makes things easier.

As I understand it POA is no longer in effect once the person dies.
Your father and aunt are joint executors not POA.
I am sure there is a document that he can file in Probate Court relinquishing being executor. This would leave your Aunt as sole executor. I doubt you could be appointed as joint executor as this is done by the person making the Will.**

**I am not a lawyer and I am sure one will respond with a much more knowledgeable answer

If your father and aunt are joint executors, your father can probably decide not to take up executorship and leave it to your aunt. Would this be acceptable? If your father has already filed for probate as an executor, I am not sure if this is still an option. Either of these, or you acting as POA on this matter, deserves some local legal advice. If the POA route is the one, it needs to be specially drafted to apply only to this responsibility, and not to require your father to have lost competence first. With any option, you need a local lawyer. Best wishes.

Is your dad an Executor of the Estate? If yes, you will need to check if your father can assign his duties to a POA.