All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
If it is true that your wife is having an affair with her nephew, then she is committing a grave sin. This is considered incest, which is graver and more serious than adultery, as was stated by the scholars. Al-Haytami said, “Incest is absolutely the gravest category of zina (fornication or adultery).” [Az-Zawaajir] You have mentioned that she actually committed incest with her nephew. If this is the case, then they have fallen into the trap of the Devil; verily, he gradually leads people to their own destruction. Allaah, The Exalted, says (what means): {...and do not follow the footsteps of Satan. Indeed, he is to you a clear enemy.} [Quran 2:168]
It is incumbent on her to turn to Allaah in sincere repentance; the conditions of repentance were underlined in fatwa 86527. If she repents to Allaah, then you should conceal her sin. The Islamic sharee'ah encourages the concealment of the sins and faults of fellow Muslims, especially if they repented to Allaah, The Exalted. Ibn ʻUmar reported that the Prophet, sallallaahu ʻalayhi wa sallam, said, “Whoever concealed the faults of a Muslim, Allaah will conceal his faults on the Day of Judgment.” [Al-Bukhari and Muslim] Hence, you should conceal her sin and refrain from informing anyone of it unless there is a guaranteed benefit for disclosing this information, such as telling someone who could deter her from committing such a sin, like a guardian or a person in authority. Ibn ʻAbd Al-Barr wrote, “It is also deduced from the hadeeth that it is obligatory on the Muslim to conceal his sins committed in secret, and it is also obligatory to conceal the sins of others as well...”
As for informing her children of her sin, this would most likely lead to evil consequences, so you should not opt for that. The fact that she is committing this sin does not constitute a religious impediment to the residence of her children with her. The Islamic sharee'ah enjoined children to show kindness to their parent even if he or she is non-Muslim. Allaah, The Exalted, says (what means): {But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them but accompany them in (this) world with appropriate kindness ...} [Quran 31:15]
Allaah knows best.