The relations between the spouses should be based on tranquility, love and mercy as Allah says, (And among His Signs is this, that He created for you mates from among yourselves, that you may dwell in tranquility with them, and He has put love and mercy between your (hearts): verily in that are Signs for those who reflect.) (Ar-Rum 30: 21)
Tranquillity (sakan), love (mawaddah) and mercy (rahmah) are very important concepts in Islam which summarize the ideals of Islamic marriage. With this in mind, it is the duty of the husband and wife to see that they are a source of comfort and tranquility for each other and to avoid disputes to the best of their ability. They should do everything physically, emotionally and spiritually to make each other feel happy and comfortable. Above all, divorce should be the final resort.
The case referred to in the question is not a proper form of khul`, as in khul` the wife redeems herself from her husband through paying him the dowry he gave her or its value. The situation mentioned in the question is a form of revocation, and to achieve the proper form of khul`, there are certain procedures that should be followed.
Sheikh `Abdullah Al-Judai`, Member of the European Council for Fatwa and Research, states the following:
I believe that the following procedures should be done in this case and in similar ones:
a. The spouses should resort to two Muslim arbitrators—one from the husband’s side and the other from the wife’s side, even if the husband does not agree. Almighty Allah says,
(And if ye fear a breach between them twain (the man and wife), appoint an arbiter from his folk and an arbiter from her folk. If they desire amendment). (An-Nisaa’ 4:35). In case reconciliation is not reached, the two arbitrators may separate the spouses.
b. If that is difficult and the wife is in a country where there is an Islamic judiciary, she must not go beyond it. This is possible in some cases, as far as we know, especially if the marriage is registered in an Islamic country. The wife can do that in those Islamic countries even by proxy.
c. If the wife has no other alternative except to resort to the civil law of the country where she is staying, there is no objection to her doing so, even if the judge is not a Muslim. Compelling a husband to revoke a marriage contract is not executed except by the two arbitrators or the ruler; so if the arbitration of the two arbitrators or the Muslim ruler is not possible, there is no objection to resort to a non-Muslim ruler (judge).
The European Council has previously made a decision regarding the dissolution of marriage by a non-Muslim judge as follows: The original ruling is that a Muslim must not refer his cases except to a Muslim judge or to one acting on his behalf. However, due to the absence of an Islamic judiciary for Muslims to resort to within the non-Muslim countries, the Muslim who has concluded his marriage contract in accordance with the laws of these countries has to execute the decision of divorce made by the non-Muslim judge. Such Muslim who has concluded his marriage contract in accordance with this non-Islamic law has implicitly accepted its results, among which are that the marriage contract is not cancelled except through the judge. This can be considered as an authorization from the part of the husband, which is permissible in the Shari`ah according to the majority of its scholars, even if he does not declare this, for there is a juristic rule which says, “What is conventionally known is like what is stipulated.” In addition, executing judicial decisions, even if it is not Islamic, is permissible, as it can be considered a sort of preserving interests, avoiding evils, and putting an end to chaos. This is stated by more than one prominent scholar, such as Al-`Izz ibn `Abdus-Salam, Ibn Taymiyah, and Ash-Shatibi.