How can I move my Dad to a closer place without POA?

Your profile says Dad has diabetes and you don't mention dementia. If Dad is mentally with it enough to understand what it means to allow you to act on his behalf, instead of his brother, then all he has to do is change his POA to you.

But really, the POA cannot determine where the person lives. So if it would be more convenient for you and you could visit him more often and Dad is willing than you can move him without having POA. And if Dad isn't willing to move, then POA is not enough for you to force him to. That would require guardianship.

Because of the POA's health and distance from Dad, I think it would be a very good idea for Dad to change the POA to you. But that might not really have a lot to do with moving him.

I'm sorry to hear about your uncle. It sounds like your dad needs to make you his POA. That's possible only if he is still competent.

How far away do you two live now?

Ask the doctor at his current nursing home for his opinion about moving him to another facility and he could write up an order to help make that happen.