Look at it this way:
Your friend A has got herself into a financial mess through trying to help her daughter pay for a divorce.
Now A is forced to sell her house.
A's daughter who has accepted her mother's help to pay for a divorce, plus to pay her own mortgage refuses to let A move into her house.
A is now desperately trying to get you to let her move into your house.
You have no desire to let her in and I can honestly see no reason why you could possibly be expected to do so.
At this point B a mutual friend of yours and A sticks her oar in. Why? If she is so concerned about A, let her offer A a home.
B has no right whatsoever to interfere and attempt to make you feel guilty.
There are three selfish people here: A, her daughter and B.
Please do stick to your decision not to house A. You do not need to state your reasons. Just tell A that it is not possible.
You might well find yourself being taxed on a supposed income from renting out part of your house if you did accede to this unreasonable request, or be denied a carer, should you one day need one, on the grounds that A could take care of you.