Rather, I get the sense that her mother's overprotectiveness is because Yuki has been so traumatized by her condition.
That, too - it's not hard to see how and why she seems to have turned out a bit neurotically (and probably suffocatingly) overprotective. There's hints of it in their conversation too ("then I can't protect you" etc.).
The best intentions behind it doesn't make it any less problematic for Yuki's personal developement ofc but that sort of thing happens a lot between parents and children.
On an entirely different note Yuki seems to take a lot after her mother physically (even their eyelashes look similar) - pretty face and flat as a board :v