Is it better for a man to divorce his second wife with whom he quarrels, so that she can have some peace?
Question

                Is it allowable for a husband to divorce his (second) wife without her doing anything wrong?  This man found out that he does not have much in common with his wife, often fights with her and dislikes things about her through no fault of hers.  Would it not be better to let her free to marry someone who would love her and cherish her than to keep her in a much-less-than ideal situation?
Praise be to Allah.
    The man has to treat both of his wives 
    fairly, and to fear Allaah with regard to them. The woman should resist her 
    jealousy and strive to control herself (jihad al-nafs) and not cause 
    trouble to her husband because he has another wife.  

    “The basic principle concerning divorce is 
    that it is makrooh (disliked), and if we say that the basic principle 
    is that it is forbidden, this is not far-fetched. This is indicated by the 
    words of Allaah concerning those who take an oath not to have sexual 
    relations with their wives. He said (interpretation of the meaning):  
    

    ‘… then if they return (change their idea in 
    this period), verily, Allaah is Oft-Forgiving, Most Merciful. 
    

    And if they decide upon divorce, then Allaah 
    is All-Hearer, All-Knower’ 

    [al-Baqarah 2:226-227]
The aayah ends with 
    these two names, ‘All-Hearer, All-Knower’, if they decide upon 
    divorce, to indicate that Allaah does not like that, because in the case of 
    one who returns or comes back to his wife after swearing not to have 
    intercourse with her, it says that ‘Allaah is Oft-Forgiving, Most 
    Merciful.’  

    This makes it clear that Allaah likes the one 
    who has sworn such an oath to go back (to his wife). In the case of one who 
    has decided to divorce his wife, the use of the words 
    
    ‘All-Hearer, All-Knower’ indicates that Allaah dislikes that. It 
    was narrated that the Prophet (peace and blessings of Allaah be upon him) 
    said: ‘The most hated of permissible things to Allaah is divorce.’ This 
    hadeeth is not saheeh, but its meaning is saheeh. Allaah dislikes divorce, 
    but He does not forbid it to His slaves, to make things easier for them. If 
    there is a valid reason for divorce, in sharee’ah or otherwise, then that is 
    permissible. Whether there is a valid reason depends on whether the woman’s 
    remaining married will lead to some shar’i reservation that can only be 
    alleviated by divorce, then he may divorce her, such as when the woman is 
    lacking in religious commitment or chastity, and he is unable to reform her. 
    In such cases, we say that it is better for him to divorce her. But if there 
    is no such valid reason, whether shar’i or otherwise, then we say that it is 
    better not to divorce her; indeed in such a case divorce would be makrooh.”
    

     (As’ilat al-Baab al-Maftooh by Ibn 
    ‘Uthaymeen, p. 113) 

     With regard to the woman mentioned in the 
    question, if she is able to live with her husband in a good manner, and if 
    each of them can put up with the other at times of short-lived anger, then 
    this will be better for her, for him, for their children and for the family 
    of each partner. If a good life cannot continue between them for some reason 
    on the part of one or both of them, and it appears that separation is better 
    for her or for him or for both of them, then Allaah says (interpretation of 
    the meaning):

     “But if they separate (by divorce), 
    Allaah will provide abundance for everyone of them from His Bounty” 
    

    [al-Nisaa’ 4:130]

    Allaah may provide her with a husband better 
    than him, who will be more righteous and treat her more kindly. May Allaah 
    help us all to do that which He loves and which pleases Him.