Hi feellost,
It is interesting that you have this issue with your Mom. I always wonder what is like for a woman with dementia. You see, my father-in-law has been a widower since late 2004. At the beginning he was not diagnosed with Alzheimers (now he has late Alzheimer's) yet until late 2006. During the whole time from 2004-2010, he has been wanting a wife! The lady friend would be his future wife, the caregiver is his wife and the nurse is his wife! Any lady that stays long enough with him has the potential to be his chase! In 2007 when we visited him, I saw he had viagra in the fridge! Oh my. It was an old one and he forgot about it. I threw it out. Now he is totally incompetent.
He has been like a womenizer but new people see him as a gentleman!!
Somehow he didn't really elaborate like your Mom did, but he once said "how come she didn't want to sleep with me?"

(with this black young caregiver.)
Like your Mom, he has been able to talk to my husband bluntly about wanting a wife and how to deal with it. The thing is it is his fantasy and no one will marry him or go to bed with him anymore.
I don't recommend that you take your Mom to a brothel. I once thought about it. Oh yeah, bring in some escort (I am just kidding).... Gradually I realized it has to stay in his fantasy and cannot be carried out!! It would only come true if he were normal, you know...
The thing is we still have to worry about sexual disease for these fragile elders.

Well, I don't like this attitute of some caregivers. They felt sorry for him and played along with him. In the end, he was very disappointed. Also why should the women be his psycho playmate? It is not decent.
So we only let it go in the air. Ok, he proposed to everyone, and they all ignored him.

One told him she is married and has kids. Well, he does not care if she was married or not! He flirted with this nurse in front of her husband who was the home care boss!!

She had to tell him she is married. Fortunately he can still take no. I do believe the "potential lovers" need to say no because he would never stop it until he goes to bed with them!
Now I think he will be more and more into it since he has stopped walking in May. We were told that we could hire a one on one caregiver to be his companion in the residential home. Well I don't want this girlfriend episode again!
In your Mom's case, I know it is different, but I think all you can do is to distract her and bring her more activities or friends. Maybe she also needs peers so maybe bring her to this day care center for the elders.
That is all I can think of.
It is not easy. All I am saying is say no gently and distract her. or say yes to her fantasy. Don't carry it out....
Maybe you can ask the doctor to prescribe some pills to reduce her desire. My FIL is taking anti-depression drug in the residential home.
Good luck,
Nina