I have a question: A man blames his wife that she has committed Zina on a Du'aa' test after 30 years of marriage and says that a handicapped son is not his and instructs the wife to stay away from him, not divorces nor does the wife ask for it as she has kids. The husband without having four witnesses as per Islaam and also now marries another woman and has a kid from her. Is it a lawful act? What can the women do?
He also turns on his other sons who want him to resolve the situation but he tells them to leave his house as they all live together is it correct?

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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions

Islam is keen on preserving the honour and dignity of the Muslims and protecting them from anything that could spoil their dignity. That's why Islam legislated a severe punishment for those who accuse a chaste Muslim, male or female, of not being chaste without evidence.

Allaah says (interpretation of the meaning): {Verily, those who accuse chaste women, who never even think of anything touching their chastity and are good believers, are cursed in this life and in the Hereafter, and for them will be a great torment,}[24: 23].

Therefore, this man is slandering his wife (accusing his wife about her chastity), thus he deserves the punishment of a slanderer unless he brings four witnesses, or that his wife acknowledges the act, or they invoke the curse of Allaah on the liar.

Allaah says (interpretation of the meaning): {And those who accuse chaste women, and produce not four witnesses, flog them with eighty stripes, and reject their testimony forever, they indeed are the Fâsiqûn (liars, rebellious, disobedient to Allaah).}[24: 4]. In Islam we do not rely on DNA testing to determine the paternity of a child. Even if DNA evidence is confirmed, it is just an indication and it is insufficient to deny one's lineage. This test cannot be used to overrule the saying of the Prophet : “The child is for the bed (i.e. what results from intercourse).” [Al-Bukhari and Muslim] So this child is the son of his father (mother's husband) because he is born on his bed and it is not permissible to deny him unless he and his wife invokes the curse of Allaah on the liar.

This woman whom he has slandered is still his wife, and he has to protect her honor if he does not bring evidence of his claim, or invoke the curse of Allaah on whoever is lying. It is not permissible for him to leave her suspended. He has either to keep her and treat her kindly or divorce her nicely. But it is more appropriate for him to keep her as he had other children with her.

If this husband persists on staying away from her without a sound religious reason, and she fears she will be harmed, then she can take her case to an Islamic court of justice so that the judge would study the case and rule according to what is appropriate.

This man should not have forced his children out of his home, and it is forbidden for him to evict the children who are still at the age of fostering and at an age their mother should provide for them, because this exposes the children to being lost or to choosing bad company.

Allaah knows best.