For everyone feeling irritated by potential rival appearance I just want to advice to not jump to conclusions. This manga already proved a few times that it’s not following usual stereotype's bullshit.
Assuming she's the step sister, the likely chain of events is [Ayako meets Akira] -> [Akira introduces Ayako to Asuka's dad] -> [Ayako marries Asuka's dad]. Given that we're told Ayako used to be an ice queen, what happened between her and Akira on the way would seem to be extremely relevant to the currently situation - including the way she views her daughter's Oedipus complex/apparent lesbianism.