Can the children of an incapacitated HOA member vote in HOA business if they have a General Power of Attorney?

I am president of the BOD in an AZ HOA. We are a 55+ community of 70 owners and have at least 4 owners who are incapacitated by Alzheimer's or similar. Their children are handling their affairs. We are soon to vote to approve new CC&Rs and new Bylaws. If these children have a General Power of Attorney, can they participate in these votes on behalf of their parent? If so, would the HOA need a copy of the GPOA?

Do what is right by the owners who are now suffering Alzheimer's or Dementia if these owners are, otherwise, upstanding owners.

Yes, the HOA should have a oopy of the POA on file. You'd want it if, for instance, down the road someone wanted to challenge the results of a vote and claimed that "unqualified persons" were allowed to vote - or for reference by future board members who were not involved in making this decision. (It can be hard for HOAs to maintain institutional memory since board members come and go.)