Yui pretty much takes care of Hana, but they are more like roommates if anything.
She feels as though Hana can't "function" in the real world.
And due to the stigma surrounding disabled people in Japan, Yui feels the need to protect her sister.
That and Hana kind of has separation anxiety. Thanks Jackass Empire.
Hana feels as though her sister is ashamed of her. She feels like she is a burden to her. She would mask in hopes of being "normal" and to shame her sister.
That would unfortunately lead to burnout and meltdowns.
Hana also gets annoyed when Yui would try to "help" her by babying her on the simplest of tasks. (It doesn't happen much anymore, but she still gets annoyed when people baby her.)
She knows Yui means well, but still.
Yui wants to understand her sister. Hana wants acceptance from hers.