Does she have the right to ask for divorce if her husband is having haraam relationships with other women?

It is not permissible for a woman to ask for khul‘ or talaaq from her husband except for a legitimate shar‘i reason, because of the report narrated by Abu Dawood (2226), al-Tirmidhi (1187) and Ibn Maajah (2055) from Thawbaan who said: The Messenger of Allaah (blessings and peace of Allah be upon him) said: “Any woman who asks her husband for a divorce when it is not absolutely necessary, the fragrance of Paradise will be forbidden to her.”.

This hadeeth was classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

“absolutely necessary” indicates a case of hardship in which divorce is the only recourse. 

It was narrated from ‘Utbah ibn ‘Aamir (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Women who seek divorce by khul‘ are the hypocrite women.”

Narrated by al-Tabaraani in al-Kabeer (17/339); classed as saheeh by al-Albaani in Saheeh al-Jaami‘, no. 1934. 

What is meant by that is women who seek divorce by khul‘ when there is no reason that makes it permissible for them to seek that. 

If the husband is having haraam relationships with other women, this is a reason which makes it permissible for the wife to seek talaaq or khul‘, so as to protect herself and her honour, and as a precaution against diseases that the husband may bring because of these relationships. 

Shaykh Ibn Jibreen (may Allah preserve him) said, explaining what justifies seeking talaaq or khul‘: If the woman dislikes her husband’s character, such as if he is harsh or hot-tempered or quick-tempered or gets angry a great deal for the slightest reason and rebukes for the slightest shortcoming, then she has the right to seek divorce by khul‘. 

Secondly: 

If she dislikes his physical make-up, such as if he has a defect or is ugly or is lacking in one of his senses, then she has the right to seek divorce by khul‘. 

Thirdly: 

If he is lacking in religious commitment, such as if he does not pray or is careless us about praying in congregation or breaks the fast in Ramadan without any excuse, or he does haraam things such as zina, drinking alcohol, listening to songs and music, and so on, then she has the right to ask for divorce by khul‘. 

Fourthly: 

If he denies her her rights to maintenance, clothing and other essential needs and he is able to provide that, then she has the right to ask for divorce by khul‘. 

Fifthly: 

If he does not give her her right to regular intimacy and that which will keep her chaste because of impotence (inability to have intercourse) or because he is not interested in her or is attracted to someone else, or he does not divide his time equally (among co-wives), then she has the right to ask for divorce by khul‘. 

And Allah knows best. End quote. 

See also the answer to question number 1859. 

And Allah knows best.