Rini idolizes Darien as the perfect guy, and she doesn't seem to focus on the fact that he will be her future father. The only thing she sees is a man who loves and takes care of her. She doesn't think,'Hey, he's my dad, I can't have a crush on him!'. She just doesn't focus on it and falls in love with her father's past self.
Rini's biggest problem is that she is small. She wants to be a beautiful adult like her mother (whom she also idolizes) and in the past, she also looks upto Serena because Serena is a grown woman who can do many things (one of them is being Darien's girlfriend)
Since in the past Rini and Serena are more like sisters than mother and daughter, it's easy to see how Rini thinks that she's better for Darien than ditzy Serena. This is all related to her desire to be adult, to no longer be a child. She wants to grow up, to fall in love, and the only man in her life to fall in love with is Darien.
She doesn't focus on the fact that he is her father. She sees Darien as Darien. To her, he's Serena's boyfriend and a man who gives her (Rini) love and attention she's never had from any man except her own father.
It's understandable that a small child will idolize and become "in love" with an older man who gives her love and attention especially when the girl feels so alone - as she first did in the past - away from her family and friends. Darien seemed to be the only one who understood her feeling of loneliness, of being orphaned (remember, he was an orphan as well).
A little girl who wishes to be adult, no longer small (she has been small for 901 years), who is placed in the past without her parents and the friends she knows and loves, this little girl proceeds to fall in love with the first guy who gives her love, understanding, and attention. She doesn't fully understand that he is her father. But she doesn't chase after him BECAUSE he is her father, she chases after him because she genuinely needs his love and affection.
All this changes though as she falls in love with Helios/Pegasus. She now has a man in her life she also idolizes and loves, and who loves her back and IN THAT WAY and who she can be with. Helios is the one who makes her feel like a woman, not like a child. Helios shows her that she is a beautiful woman, and one who has won his heart. This is something she never wished for from Darien and never would have gotten anyway.
Rini, in conclusion, is not some horny little girl. She sees Darien as her friend, needs his love and attention and in her wish to be grown up, wants to know what it like to have such an ideal man as her boyfriend. She chases Darien for who he is, as Darien, and never chases him as her father.
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