I mean it is a complicated situation for her. She wants to spend time with him and also tell him that she can't see her. I am sure though that she would completely understand it if the MC went home to his father considering how emotional she gets when he tells her about his feelings about his birthday. Taking care of family is a lot different than a friend with a cold, especially another girl. I wouldn't be surprised if she would suggest to have the date another day if that was the case.
One cool thing about this game is that you can experience the story and get vastly different views on a character depending on what choices you make. I for example have always seen the choice of getting involved with MaJo to be a very selfish decision by the MC, likely because I played DIK the first time. Even after restarting and having them accepting the MC I still see that relationship as a disaster in the making. But I know others feel differently, that the MC is what keeps MaJo together.
I agree that the recital scene is a bit odd if Jill rejects the MC at the end, I'll give you that. But in my opinion that is a flaw in the writing rather than the character.
