Praise be to Allah.
What this man did of committing zina with a married woman, then inciting her to leave her husband and ask him for a divorce is a great crime and a major sin, and it is a blatant immoral act which is indicative of the doer’s lack of religious commitment and lack of respect for the limits set by Allah, may He be glorified and exalted. That is because zina (adultery) is an abhorrent crime according to all divinely-revealed laws, as is well known, and turning a woman against her husband is a grave sin, in addition to the sin of zina. A stern warning has been issued concerning it, as in the hadeeth of the Prophet (blessings and peace of Allah be upon him): “He is not one of us who turns a woman against her husband.” Narrated by Abu Dawood (2175); classed as saheeh by al-Albaani in Saheeh Abi Dawood. Abu Dawood (5170) also narrated that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever turns a man’s wife or slave against him is not one of us.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Shaykh ‘Abd al-‘Azeem Abaadi (may Allah have mercy on him) said: “Whoever turns a woman against her husband” by mentioning the husband's bad qualities in the presence of his wife, or by mentioning the good qualities of a “stranger” (one who is a non-mahram to her) in her presence.
‘Awn al-Ma‘bood, 6/159
He also said: “Whoever turns a man’s wife against him” means by deceiving her or turning her against her husband, and encouraging her to get divorced so that he can marry her, or so that he can arrange her marriage to someone else, and so on.
‘Awn al-Ma‘bood, 14/52
What this woman did of committing zina with that man is a grave sin and a betrayal of her husband and a denial of his marital rights. The punishment of this crime for one who is married – whether a man or a woman – is stoning to death, as is well known from the mutawaatir Sunnah.
Moreover, her asking her husband for divorce when there is no good reason for that is haraam, and a stern warning has been issued concerning that in the words of the Prophet (blessings and peace of Allah be upon him): “Any woman who asks her husband for a divorce when there is no good reason, the fragrance of Paradise will be denied to her.”
Narrated by at-Tirmidhi, 1187; classed as saheeh by al-Albaani in Saheeh Abi Dawood
Some of the scholars are of the view that if a man turns a woman against her husband, it is not permissible for him to marry her; rather she becomes forbidden to him for eternity. This is the view of the Maalikis.
However the majority of scholars are of the view that such a marriage is valid, even though they have sinned by doing what they did. This has been discussed previously in fatwa no. 84849
What appears to be the case in this situation is that so long as this man regrets what he did, and the woman regrets it likewise, and they have repented to Allah, may He be glorified, from the sin of zina before marriage, then they both have to repent again, sincerely and truly, from what they did of conspiring against the first husband and breaking up his family. They should do a lot of expiatory righteous deeds, as much as they can. Allah, may He be exalted, says (interpretation of the meaning): “And perform As-Salat (Iqamat-as-Salat), at the two ends of the day and in some hours of the night (i.e. the five compulsory Salat (prayers)). Verily, the good deeds remove the evil deeds (i.e. small sins). That is a reminder (an advice) for the mindful (those who accept advice” [Hood 11:114]. And it was narrated from Abu Dharr (may Allah be pleased with him): The Messenger of Allah (blessings and peace of Allah be upon him) said to me: “Fear Allah wherever you are, and follow up a bad deed with a good deed which will erase it…” Narrated by at-Tirmidhi, 1987; classed as hasan by al-Albaani in Sunan at-Tirmidhi. It was narrated that Ka‘b ibn ‘Ujrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said to me: “Charity extinguishes bad deeds as water extinguishes fire.” At-Tirmidhi (614); classed as saheeh by al-Albaani in Sunan at-Tirmidhi.
After having repented, they do not have to separate from one another, as is the view of the majority of scholars, including the Hanafis, especially as they have children who would be adversely affected by such a separation.
For more information, please see the answer to question no. 216816
And Allah knows best.