The impression I got was that by CS4 the Hayworths (minus Colin, of course)
had
figured out that Renne was their daughter but didn't want to voice it because Renne had very obviously moved on to her new life/family with the Brights and didn't want to put everyone in an extremely awkward position because Renne seemed fine with the current distance she had with them where she was basically Colin's cool older friend/hero who did the "i was just passing through" anime shtick. But also because they didn't want to voice the idea and have Renne reject it and kind of slam the door shut on any kind of reconciliation.
but
that
very much is probably some headcanon on my part
May you find your book in this place.
Formerly known as xp1337.