Could this be a sign of dementia or, just loneliness?

Having a girlfriend while your wife is still alive but mentally incapacitated is not in itself a sign of dementia. Is your father exhibiting any other "strange" behavior? Bringing her to family events might be poor judgment, or it might be his way of demonstrating that he has made peace with his decision and is not ashamed of it.

If the family is worried about this, why not speak to him directly about it? Express your concerns and see what he has to say about it.

Usually by the time someone with Alzheimer's is in memory care they have had the disease for several years. I doubt that your parents have been happily married for 56 years. A person with dementia gradually changes from a spouse to a dependent. So perhaps your parents had 50 happy years of marriage and then another 6 years of a caregiver/dependent relationship. That relationship can be profoundly loving -- it just isn't what most of us think of as marriage. I think this is very hard for a person outside the relationship to grasp.

Oh, be patient with your father, his heart is breaking from the loss of his wife. You could ask him not to bring her to family gatherings, which is perfectly understandable.

Sounds like loneliness. Some people are just afraid to be on their own, which is understandable. Too bad Dad couldn't find some buddies to hang out with at this point in time. To bring a new girlfriend around the grandchildren [depending on the children's ages] can be confusing to them.

One thing to try is call your Dad after 4pm to see if he sounds confused. Sundowning phase of dementia is noticeable, that is when I really knew that my Dad was getting dementia. Dad would think he was still at work [he had retired 30 some years ago], and that he had missed his bus [that was back in the 1940's] so he will stay at the hotel [Memory care center where he lived]. If I had called Dad in the morning, he would have been fairly clear minded for someone in his 90's.