A brother has sexually molested his sister.

Answer

The strictest purdah for him is Waajib. He should not be considered as a brother. He is a veritable shaitaan who is capable of ravaging their chastity. He will never again be a mahram for her.

Ignore what the people say. Nabi Nooh (Alayhis salaam), despite all his efforts of centuries to guide his family, his own son and wife remained kaafir. As long as you had discharged your obligation of tarbiyat, you need not worry. Hidaayat comes from only Allah Ta'ala. Rasulullah (Sallallahu alayhi wasallam) did not succeed in giving hidaayat to Abu Taalib, the uncle whom he loved dearly. The people are juhhaal. What wrong did Nabi Nooh (Alayhis salaam) do that his son remained kaafir? People of the dunya lack proper understanding, hence they speak much drivel. Don't allow their nonsensical talks to grieve you.