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

                Is it permissible to ask for divorce from a husband who has haraam relationships with other women?.
Praise be to Allah.
      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.