Would this qualify as a complex?
I'm pretty sure this is the very definition of a complex. Sunako's extremely screwed up, with her mother beating her constantly and her father being mostly absent, she had nothing to grab ahold of; his death upended what little she had, especially with hearing that her mother wishes she had died instead.
When she's moved in with her father's other family, his wife isn't shy about letting her know that the relationship's temporary and that she's to earn her keep. She's moved up from an abusive mother, but that's about it. Only when Yasuko makes her speech on family and what it means is Sunako given something permanent to latch onto. This is, of course, why she takes everything she has to throw at her: calling her on it would risk losing the one thing she's clinging to for dear life.
There's nothing healthy here.