Is a man's marriage to the daughter of a woman with whom he previously committed adultery valid, and what is the ruling concerning their children?

Scholars have differed on the issue: Does unlawful cohabitation (zina) render lawful cohabitation (marriage) unlawful? The Hanafis and Hanbalis held that unlawful cohabitation makes lawful cohabitation unlawful, while the Malikis and Shafi'is held that unlawful cohabitation does not render it unlawful. The preponderant opinion is the latter, because Allah the Almighty forbade the wife's stepdaughter by saying: "And your stepdaughters who are under your guardianship [born] of your wives unto whom you have gone in." (An-Nisa: 23). And the woman with whom zina was committed is not a wife. Children are attributed to their father if he married believing the marriage to be valid.