No person has any rights over another's life be they married or not.
If a person is acting as an attorney under a Health and Welfare POA they can only do so when the doner has lost the capacity to make a particular decision themselves.
This still does not mean every decision as someone could be deemed to have capacity to make a minor decision but not a big one like where they live or having a major operation.
Depending on why your Mum does not want a particular visitor going to see your Dad you or she or the home could speak to SS about safeguarding. If there are concerns for his welfare by this person visiting then the family should speak to the home immediately in any case.
Just because she does not want this person to visit does not mean they can't, even if she did have POA the attorney would have to have a valid reason, it has to be in the doners best interests not the attorneys!
I hope this makes some sense, I'm just waiting for my Dad's registered one to arrive any day so have been looking at this recently, and particularly in relation to a wives rights over her husband.