The issue with Summer is we don't know what happened, so speculating is tough. We get told that her parents took her away after Nami snitched on them being at the cabin. We also learn Nika sees her one last time after this (possibly wounded/dead, who knows?).
Now the reason her parents don't want her hanging around with Nika, it's possible that it's someone that dislikes William and doesn't want their daughter being attached in any way to his offspring. The only person so far we've met in WiaB who fits the bill is Abigail, who has no problems with the other Zane's, only WZ.
Now that Ocean has retconned away the incest, we know that Ayua is likely Nika's half-sister (so no hanky-panky), Nami is the spitting image of Daphne (unlikely to be fathered by William, so

for snu-snu). I'm not convinced Zara and Vanessa share the same father, which is why the mother was so harsh towards Zara.