IMHO any option which includes allowing a person to live at home (short of actual abuse) is preferable to being forced into a care home.
A person who is clinically depressed will have little empathy with the feelings and needs of others. Someone with Asperger's, doubly so. It is known that they do not pick up on the normal clues that most of us use to communicate with each other, body language, gestures etc.
I would suggest option 2. Why should this nice intelligent elderly lady be forced to leave her own home just because of another person, B?
'A falling housing market' - indeed. Round here no houses are selling, not at all! FTBs have disappeared, unable to get mortgages with the deposits now required. Everyone else is waiting to see how far property values will fall, in the hope of picking up a bargain.
Just a few thoughts.