Devil is always in the details ...
My Mom lives with me part of the year in North Carolina and my brother for part of the year in Delaware. We both want to have the POA to make things easy for whoever has her, at the time. Is it possible with 2 different agents and 2 different states?
Only a qualified attorney should be involved in addressing a document which includes a joint proxy situation.
I highly recommend using a certified elder law attorney for this, you can find one near you or brother at www.nelf.org.
If mom is kinda sketchy at times in understanding what is going on, be sure and schedule the attorney for her best time.
The problem with you having one for your state and brother having one for his state, is that the newest one cancels out all others prior to that date. Far better to have one with both of you able to act.
Everyone demanded a POA that has the law firm's official stamp on it. Please have it done with a lawyer. It's worth the money.