I live in New York, my mother lives in Alabama. I was told by a Lawyer that I cannot get a POA because I don't live in Alabama. Correct???

Ask the lawyer if there is an alabama law that disallows POA in another state. I would be surprised. But, there are some strange laws in the south.
if dad is incapacitated in any way, he cannot assign PO A to anyone. You would have to go the guardianship route.

The one who lives closest to Mom should have POA. And since she lives in Alabama IMO thats were she has it written up and assigned. But as said, she has to be competent to assign someone. She can assign a main person and a secondary if the main person can't carry on the responsibility.

There are lots of people on this forum who do not live in the same State as a LO and are POAs.

I'd say that lawyer graduated in the bottom of his class. You can assign power of attorney to any competent adult.

This website doesn't mention anything about where a POA must live.

https://www.alabamalegalhelp.org/resource/powers-of-attorney

Momma assigned me POA after we lost dad over 10 years ago and we were redoing her will. I am not the closest but the most responsable one and I live out of state. As long as she is compendent she can assign anybody she wants too.

If your mom is cognizant she can assign POA to whomever she wants to.
If your mom is not cognizant then she can not assign POA to anyone no matter where they live.
Has the lawyer told your brothers the same thing?
You might want to consider Guardianship. The ideal thing would be to pick one sibling to be Guardian or you could try Co-Guardianship. (would work as long as you all get along and all agree on everything when it comes to mom's care)

If mom is cognizant taking her to a lawyer when you are there next and she can complete paperwork assigning POA. Strongly suggest a lawyer that is well versed in Elder Care Law.
If mom is not cognizant bring her to the lawyers office and begin Guardianship

Forgot to mention. Not only do I live in GA and momma lives in AL and I am out of state we used momma and dad's attorney in AL because at that time I was executor of dad's will and we were working on mommas. Attorney did not have a problem that I was out of state. Now I can see that is a problem for me because I am doing the driving back and forth but I am the responsible one. Siblings don't want any part of any of it except their inheritance.