Is it permissible to reconcile with the brother who molested the questioner's daughter, and is she required to offer an expiation for an oath (kaffarat yamin) after shaking hands with him, and what is the ruling on her not forgiving him?

If the uncle's practices with his niece are confirmed, this is a grave transgression that necessitates repentance and protecting the daughter from mingling with him. It is permissible to shun the disobedient person if that would have an effect on him. It is not permissible for a woman to shake hands with a man who is not a mahram. Rather, it is better for her to expiate for her oath regarding visiting her uncle's house and communicating with his wife, by feeding ten poor persons, or clothing them, or freeing a slave, or fasting three days if she cannot find any of these.