Blanche didn't know how to deal with Jane
She might have saved herself from a lot of the abuse she went through in this film if she had altered her behavior slightly. A lot of Jane's anger towards Blanche came from the fact that Blanche treated her almost like a mentally unstable child (which, deep down, Jane was). "Who are you trying to help Blanche?! What did you have in mind for me after you sold the house, some nice little place where they could look after me?!" Jane was smart to catch on to Blanche's perception of her. She knew Blanche's kind, actress-like behavior was insincere. But there are a few things Blanche could've done to avoid some of Jane's more violent outbursts.
First of all, enough with the damn BUZZING. She does it so much and it's so unnecessary in some scenes. It's enough to push even a psychologically stable person over the edge! The buzzing is what really causes Jane to flip out when she starts crying in front of the mirror. But why did Blanche need to snap Jane out of it? So what if Jane is playing the piano and singing a song from her childhood? That was probably the only thing aside from heavy drinking which gave her any pleasure in life. Look at how happy she is when Edwin comes over and she's able to perform for him. Even though she's terrible, Edwin is still kind enough (well, manipulative enough) to 'pretend' praise her. And that's all that poor Jane wanted. Just a little attention and praise for something she was once good at. Blanche could have played this game too. She could've said, "Jane, remember those songs you used to sing? Would you sing one for me now?" Perhaps, if Blanche went about it the right way, they could've "been friends". Blanche AND Elvira should have been more accepting of Jane's role as 'Baby Jane' . Jane was like a child constantly wanting to play 'dress up' but constantly being denied by the adults around her.
Anyway, I'm rambling now. I'll end with this - "We're sisters, Elvira. We know each other very well." I'm not sure about that. I think Jane knew Blanche a lot better and once the ball was in her mentally unstable court, everything went to chaos in that house.