My mother is requesting a DPOA. We live in different states is this even possible?

You may want to consider a geriatric care manager that would be the feet on the ground if needed to help you.

Her youngest brother lives in the same state, however she refuses to discuss these matters with him.

It's possible, but it is more difficult than if you live nearby. If there comes a time you have to take financial responsibility, you'll have to have them send bills, etc., to you. Many places will deal with you over the phone if you tell them you are POA. Other places are more picky. Many people find a way to work around these things. Does your mother have anyone she trusts completely who lives closer?