Is saying: "We doubt she wants to commit zina (fornication/adultery)," or "Yes... on my responsibility (I swear by it)" considered slandering chaste women (qadhf)? And what is the method of repentance, and how can her right be restored without directly asking for forgiveness to avoid family conflict?

The fundamental principle concerning a Muslim is that they are innocent and good assumptions should be made about them. Allah has forbidden ill-will. This is even more emphasized regarding a father and his brother's wife. The matter becomes more serious if the accusation is of adultery, as it may lead to slandering (qadhf), which is a grave sin, and the father's visit to his brother's wife and sitting with her while she is adorned does not necessarily mean committing indecency. Islamic law has strict conditions for proving adultery. Merely suspecting that she desires to commit adultery is not qadhf, but it is considered backbiting (gheebah) for which repentance is due, and supplication and seeking forgiveness for the one who was backbitten are sufficient.