A man doesn’t want to live with his wife but
    doesn’t want to divorce her for the sake of the children
Question

                A man has in the past had some major
      problem with his wife. Neither she, nor he want divorce as they have 3 children, yet he
      cannot live with her and has left the country. He would like to remarry in the new country
      of residence, but is afraid of the condition of equity of time between the two wives and
      that he will be called to account for it before Allah. His wife will not willingly
      relinquish her rights as she wants him to return to her, nor will she accept a second
      marriage... Is it halal for him to tell her that he will retain her as a wife only under
      the condition that she relinquish her rights to his time to a second wife? He does not
      want to oppress himself nor does he want to oppress her.. what are his options?
Praise be to Allah.If he has no interest in his present wife, there is nothing wrong with
    divorcing her and marrying another, but if he and she come to an agreement whereby she may
    remain his wife for the sake of the children, there is nothing wrong with this either. If
    he gives her the choice between divorce and giving up her rights to his time and his
    spending on her, in whole or in part, this is not oppression. Oppression is when he keeps
    her by force without giving her any of her rights whilst at the same time refusing to give
    her a divorce.
The evidence (daleel) that the situation described above is
    permissible is to be found in the hadeeth narrated by Imaam al-Bukhaari from
    ‘Aa’ishah (may Allah be pleased with her), which comments on the aayah
    (interpretation of the meaning): “And if a woman fears cruelty or desertion on her
    husband’s part…” [al-Nisaa’ 4:128]. She said: “This
    was a woman who was married to a man who did not care for her, so he wanted to divorce her
    and marry someone else. (According to another report narrated by al-Bukhaari she said: He
    was a man who saw something he disliked in his wife, so he wanted to divorce her.) She
    said to him: ‘Keep me, do not divorce me. Marry someone else and I will absolve you
    of your obligation to spend on me and share your time with me.’ This is what Allaah
    referred to when He revealed the aayah (interpretation of the meaning): ‘…
    there is no sin on them both if they make terms of peace between themselves; and making
    peace is better…’ [al-Nisaa’ 4:128].” (Reported by
    al-Bukhaari, 4807)
    “This was a woman who was married to a man who did not
    care for her” means that he did not love her or want to treat her well or stay with
    her. “I will absolve you of your obligation towards me” means: leave me without
    divorcing me. Concerning this issue, Allaah revealed the words (interpretation of the
    meaning): “And if a woman fears cruelty or desertion on her husband’s
    part…” [al-Nisaa’ 4:128]. ‘Ali reported that this was
    revealed concerning a woman who is married to a man and does not want to leave him, so
    they come to an agreement that he will visit her every three or four days.” 
Al-Tirmidhi reported via Sammaak from ‘Ikrimah from Ibn ‘Abbaas
    that he said: “Sawdah was afraid that the Messenger of Allaah 
 (peace and
    blessings of Allaah be upon him) would divorce her, so she said: ‘O Messenger of
    Allaah, do not divorce me; give my day to ‘Aa’ishah.’ So he did so. Then
    this aayah was revealed.” Al-Tirmidhi said: “(This is) hasan ghareeb.”
    I say: there is corroborating evidence in a hadeeth from ‘Aa’ishah narrated by
    al-Bukhaari and Muslim, without referring to the revelation of the aayah. (From Fath
    al-Baari).
The hadeeth mentioned by al-Haafiz ibn Hijr (may Allaah have mercy on him)
    is in Sunan al-Tirmidhi, 2966, where it is reported that Ibn ‘Abbaas said:
    “Sawdah was afraid that the Prophet 
 (peace and blessings of Allaah be upon him)
    would divorce her, so she said: ‘Do not divorce me. Keep me and give my day to
    ‘Aa’ishah.’ So he did so, then Allaah revealed the aayah: ‘…
    there is no sin on them both if they make terms of peace between themselves; and making
    peace is better…’ [al-Nisaa’ 4:128]. So whatever they agreed upon was
    permissible.” It is as if the last sentence was the comment of Ibn ‘Abbaas. Abu
    ‘Iesa said: this is a hasan ghareeb hadeeth.
Al-Mubaarakpoori said, commenting on this hadeeth:
‘Sawdah was afraid…’ This refers to Sawdah bint Zam’ah
    ibn Qays al-Qurashiyyah al-‘Aamiriyyah. The Messenger of Allaah 
 (peace and
    blessings of Allaah be upon him) married her in Makkah after Khadeejah had died, and
    consummated the marriage there. The scholars agree that he consummated his marriage to her
    before he consummated his marriage to ‘Aa’ishah, and she migrated to Madeenah
    with him. She died at the end of the khilaafah of ‘Umar ibn al-Khattaab.
‘…was afraid that the Prophet 
 (peace and blessings of
    Allaah be upon him) would divorce her, so she said…’ Al-Bukhaari and Muslim
    reported from ‘Aa’ishah that Sawdah bint Zam’ah gave her day to
    ‘Aa’ishah, so the Prophet 
 (peace and blessings of Allaah be upon him) used
    to give ‘Aa’ishah her own day and that of Sawdah. Al-Haafiz said in al-Fath:
    Abu Dawood reported this hadeeth (from ‘Aa’ishah): ‘The Messenger of Allaah
    
 (peace and blessings of Allaah be upon him) never used to prefer any of us over
    others in sharing his time (i.e., he was fair in dividing his nights among his wives, and
    each one of them had her allotted night). When Sawdah bint Zam’ah grew old and feared
    that the Messenger of Allaah 
 (peace and blessings of Allaah be upon him) might
    divorce her, she said: ‘O Messenger of Allaah, my day is for
    ‘Aa’ishah,’ and he accepted this from her. Then concerning this and similar
    cases, the aayah was revealed (interpretation of the meaning): ‘And if a woman fears
    cruelty or desertion on her husband’s part…’ [al-Nisaa’ 4:128]. These
    reports agree that she feared divorce and so gave her day to ‘Aa’ishah.
Then al-‘Allaamah al-Mubaraakpoori said: The aayah may be explained
    thus: ‘If a woman fears’ means if she expects. ‘Cruelty’ means
    that he spurns her by refusing to sleep with her or by spending less on her than he
    should, because he dislikes her and wants to marry someone more beautiful. ‘Desertion’
    means that he turns his face away from her. ‘There is no sin on them both if they
    make terms of peace between themselves’ means with regard to the sharing of his
    time and his spending on her, i.e., he should still give her something in this regard
    (sharing time or spending) in order to preserve the relationship: if she accepts, this is
    OK, otherwise the husband must either give her her full rights or divorce her. ‘Making
    peace is better’ means better than separation, cruelty and desertion. Whatever
    they agree upon between themselves is permissible.
(Tuhfat al-Ahwadi Sharh Jaami’ al-Tirmidhi).
And Allaah knows best, May Allaah bless our Prophet
    Muhammad.