This.. Actually i'm not sure too, but from what i understand the "past life" in chap2 means at the beginning of her transmigration she does'nt remember that she came from modern world.. But then after 2 years she got together with ml the memory came and then as the story goes... correct me if i'm mistaken.. (=・ω・=)
What do you mean by "he made it obvious that he abandoned her?" As I said, he did not abandon her. He was on her side the entire time. He didn't hide his love from her either. She just misunderstood his actions. He also thought that she was scared of him because of what she saw when she was small child, so he approach her with caution which she also misunderstood as him being cold. The problem here isn't that he abandoned her, it's that they had the completely wrong idea of each other and it had dire consequences.
I'm not really in love with the father character myself tbh. Yeah, it's nice watching him try to express himself for MC I suppose - buuut then I'm reminded that he's the same person who emotionally neglected his child (even if there is a valid reason behind it) to the point where the brief affection he expresses feels as if it's a threat or has a dark meaning behind it (like the knife in the first chapter imo). It's just really sad to me, particularly for the ogMC that died coveting for any semblance of love.

Maybe this will contradict with your opinion, but truthfully i feel unfair for the original character not the 'she' who have transmigrated. I mean like seriously you abondon your daughter at a very young age, she just wants your affection and love dude? I actually blame the father even hate.. Just how could you do that? How do you expect when she grew up without care from her beloved.. She just want you to notice her, she longed for love. I dont care whatever reason behind it that could bring you to do that to your own daughter. But, for me you are bullying your own daughter. This is emotional abuse. I feel bad for her. Instead of being affectionate to your own original daughter, you rather love the 'she' that who knows where she came from..