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If you ask me, the two have a sort of mother-daughter relationship more than one between two siblings, or even lovers. I think it's very obvious that Ui took over her mother's role when she wasn't around and it can be argued that Ui might even (subconsciously) think of Yui as her own daughter rather than her older sister.
From Yui's POV, I think it's highly likely that she has begone to see Ui more as a mother figure than anything else. When Yui brought home all those animals from the clubroom (S2E2, iirc), we saw that there are times where Yui even fears Ui (she practically cried and panicked when Ui encouraged her to clean up her room, much like a child would when its mother would do that). if that's true, then I wonder if Ui would actually go so far as to discipline/punish Yui for disobeying her.
Earlier in the show (S2E10), we have Yui asking Ui what she'd be like if she were to grow up. I found it interesting how Ui skillfully dodged the question and quickly changed subject. And I think the reason is simple: she doesn't want Yui to grow up, as that mean she'd become more independent and that she wouldn't need her sister to do everything for her anymore. Again, this is like a mother having to see her child become less dependent on its mother when it grows older.
At the very least it's clear that Ui is holding Yui back, at the cost of her own well-being. S2E18 showed us that Ui would risk her own health to prevent her sister from (potentially) harming herself. I think that desire to protect Yui at all cost is a sign that Ui doesn't fully trust Yui and wants to be sure that she doesn't do anything stupid or dangerous.
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