According the tree, the father first had two daughters, forehead-chan and this other girl's mother, then the same father had her with her own daughter; however, according the previous conversation the father had forehead-chan with his wife and this younger girl with his mistress. The inbreed part mentioned later (how she's whiter) would make sense if he was born as a result of an incestuous relationship (and "mistress" would be simply "not the one married with"). Take it however you want with the current info, but half-sisters is because they share one parent.
@GoggledAnon is the "imouto" (the one the landlord is having sex with and is asked to become her daughter) the result of a father-daughter pregnancy like the graph suggests or something else?