The thing with Yūka telling Ayaka that she doesn't believe her on Day A is that her actions make no sense if she doesn't believe her, but, if you accept she believes her entirely and with total confidence, her actions immediately make sense.
Yūka gets into a yelling match on Day A where she tells her that she isn't believed even by her while belittling and hurting her (emotionally) knowing that, by hearing about it on Day B and changing her actions, she can suffer minimal consequences from this.
Then, on Day B, she acts concilliatory, but uses the fight the previous day to make wholly clear that, if she is to be believed, her logic dictates that Ayaka should not get close with anyone but Yūka. And, through this, she forces Ayaka to speak to her emotions about the fight because she knows that Ayaka's answer will be one of fear of losing her.
She is, essentially, grooming Ayaka, here. She's saying that she'll be there for Ayaka and love Ayaka and believe Ayaka no matter what, but she's doing it in a way that makes clear that all of this requires Ayaka to be wholly dependent on her and have no one else and that, if she does lose Yūka, everyone else would not believe her and would not stay with her the way Yūka will.