Does anyone know if when I draw up a POA and want to add my sister, she has to be present?

What's important is where the primary person lives. If she lives in Greece, then follow the laws for her location, which may or may not require the POA's to be present. The Italian consulate there may have additional rules for protecting Italian citizens.

So, you are an American but you, your husband, and your mother (who is an American also) live on the island of Rhodes, Greece.

You can't live with her and she does not want to live with you, but you are the only child who lives nearby.

On top of that she's in denial concerning her health. Also, your mom has alzheimer's / dementia and has short term memory loss, and constantly repeats herself and loses things.

I am so glad that you described your entire situation on your profile. That is very helpful to get the bigger picture.

My first question is one concerning competency. '

Is your mother competent to understand and sign a POA document giving you durable and medical POA over her. She must be competent to do this. Your sister does not need to be present, but and absentee POA out of the country can't do much.

What are the laws concerning a non-citizen in Greece being given POA by another non-citizen.

If your mother is not competent to sign these documents, then you are really in a bind. I have no idea what the laws are in Greece about a POA or what the laws are if the person is not competent to sign a POA in Greece.

Ya'll have dual citizenship of America and Italy?

I think you best see a lawyer in getting this put together..

I mother is still competent, that's whay I want to do it as soon as possible as I don't know how long that will last. And my mother and I are also Italian citizens, so part of EU so I don't think that will be a problem. And my husband is Greek. Thanks.