Firstly: 

It is unfortunate that states that are supposedly Muslim are fighting Islam and putting pressure on Muslims with regard to their rituals and obedience to their Lord. At the time when these states are opening the door wide to corruption, immorality and promiscuity, we find that they are putting severe pressure on those who want to engage in plural marriage which Allaah has permitted. Some of theses states ban it altogether, and some stipulate that the first wife should give consent – and what wife would agree if it were suggested to her? – and some of them stipulate an income that many cannot attain even though they can afford to take another wife. 

These states should fear their Lord and avoid going against the laws of Allaah. It is not permissible for any scholar or judge to accept this legislation. If there is some misconduct and wrongdoing on the part of some of those who have more than one wife, you will also find much more misconduct and wrongdoing on the part of some of those who have only one wife, so will this lead them to ban marriage to the first wife too? 

It is strange that these laws allow that which is haraam and do not regard it as a crime or an evil, but they forbid that which is halaal and regard it as a crime. This man whom you asked about, even though he had an illicit relationship with this woman before he married her, if news of that relationship had reached the authorities they would have permitted it so long as it was with mutual consent and the woman was of sound mind!! But if he takes her as a wife this is what they regard as forbidden and wrong, and they say: It is permissible for you to take her as a girlfriend but it is not permissible for you to take her as a wife! How bad is their judgement. 

In the face of these false laws that wage war against the laws of Allaah, there is no sin on the Muslim if he uses tricks to get around them. 

If a man wants to take a second wife and he produces a forged paper in order to do the marriage contract, there is no sin on him, because the law that is preventing him from taking a second wife is a false law, and the Muslim is not obliged to obey it or submit to it. But the husband should examine the effects that are likely to result from this action, because it may lead to many bad or harmful effects. 

There is also no sin on the family of the second wife who knew of this forged paper and gave their daughter to him in marriage; undoubtedly this is better for them and their daughter and her husband than remaining in an illicit relationship. 

Secondly: 

The father should not force his son into a marriage with a woman whom he does not want, and the son should not obey him in that case, because in this case there will never be any love, compassion and kindness between the spouses, rather the husband may mistreat his wife because he dislikes her, and such marriages often end in failure and the spouses go through a lot of problems and the children suffer a great deal as a result.  

Nevertheless, the woman has done nothing wrong for which she deserves to be mistreated because he was forced to marry her. If he wants to please his father then he should treat his wife kindly and give her her rights, and accept her as a wife who has full rights to be treated kindly. If that does not happen and he is not able to keep her in a proper manner, then he should let her go in kindness by divorcing her and giving her her rights in full, with no shortfall. 

If the woman wants to stay married to him and be maintained by him, and to have him care for her child without any intimacy between them, then it is permissible for her to accept that. The same applies if he suggests that to her and she agrees. 

It was narrated from ‘Aa’ishah (may Allaah be pleased with her) (concerning the verse) “And if a woman fears cruelty or desertion on her husband’s part, there is no sin on them both if they make terms of peace between themselves; and making peace is better. And human inner-selves are swayed by greed. But if you do good and keep away from evil, verily, Allaah is Ever Well‑Acquainted with what you do” [al-Nisa’ 4:128] that she said: This was revealed concerning a woman who is married to a man, and has been with him for a long time, then he wants to divorce her, and she says: Do not divorce me; keep me and you have no obligation towards me. Then this verse was revealed.

Narrated by al-Bukhaari (2318) and Muslim (3021). 

According to a report narrated by al-Bukhaari (2584) ‘Aa’ishah said: This refers to a man who sees something in his wife that he dislikes because of old age or something else, so he wants to leave her, but she says Keep me, and give me whatever you want. She said: There is nothing wrong with that if they both agree. 

Ibn al-Qayyim (may Allaah have mercy on him) said: 

If a man is no longer interested in his wife and he does not like her any more, or he is unable to give her her rights, then he may divorce her or he may give her the choice: if she wishes she may stay with him and have no right to a share of his time or intimacy or maintenance, or she may have some of that, according to whatever she agrees with him. If she agrees to that then it is binding and she does not have the right to ask for it after agreeing to something.  

This is in accordance with the Sunnah and it is the correct view; no other view is justified. The view of those who say that her rights may be restored and she may recant this whenever she wants is wrong, because this is a deal where one party has given up something in return for something else. Allaah has called it a sulh (amicable settlement), and it is binding, as is any settlement concerning rights and business deals. If she was able to demand her rights after that, this would just delaying the problem without solving it, and this is not a settlement, rather it is a recipe for greater problems, and sharee’ah would not call for that. One of the signs of the hypocrite is that when he makes a promise he breaks it, and when he makes a pledge he betrays it. 

Zaad al-Ma’aad (5/152, 153). 

Shaykh al-Islam Ibn Taymiyah said something similar in Majmoo’ Fataawa Ibn Taymiyah (32/270). 

Thirdly: 

You say in your question that he was in an illicit relationship with her. If that means zina, then you should note that the marriage of a zaani or zaaniyah is not valid unless they repent. This has been discussed in the answers to questions no. 11195 and 14381. 

And Allaah knows best.