Shishunki Miman Okotowari(1990)

Higuchi Asuka's mother dies shortly after she tells her teenage daughter who her father is. Only knowing the family name “Sudou”, Asuka goes in search to find her absent father.

On her journey, she finds a guy being rather rough with a younger girl. Unable to resist, Asuka steps in by battering the guy with her motorcycle. When she discovers it was a big misunderstanding (Manato was just trying to get his sister Kazusa to go home), she drives them back to their house.

Once there, Asuka finds out that Manato and Kazusa are the Sudou family she's been looking for, but the father isn't there, not to mention their mother also being dead since long ago. With no other leads, Asuka decides to move in as Neesan (the big sister) until their father shows up. Things get tricky when love builds within the complex family relationship...