"And I still can't believe Blanche felt that she couldn't have sold shares of her house to the girls. I mean, really?"
Well, in real life, it could create problems down the line. For instance, selling the house would be more complicated, because all four of them would have to agree to do it, and on what they would accept.
To me, the logical thing to do in real life would be to put all their names on the mortgage for a token "sale price' of a dollar each or something, and then Blanche would still retain complete control of the house legally, and be entitled to make any and all decisions about it.
But it was very unrealistic for Blanche to tell the girls "now you have equity" without any mention of them putting any money into buying the house. That situation made no sense to me.