All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is impermissible for the woman to ask for Khul‘ without a legitimate reason. Thawbaan narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said: “Women who request Khul‘ (for no valid reason) are hypocrites.” [At-Tirmithi]
If what you said about your wife is true, then she is a recalcitrant wife. The religion clearly underlines the way to deal with the wife’s recalcitrance; please refer to Fatwa 85402.
You may convince your wife to change her mind about Khul‘ by seeking the mediation of wise family members on your side and on hers; they may try to reconcile between you on sound basis that would help you have a stable marriage and avoid problems in the future.
It should be noted that Muslims should refer their disputes to legitimate Islamic courts only; if this court is run by man-made laws, it is impermissible for Muslims to refer their disputes to it in the first place. The verdicts pertaining to divorce or Khul‘ issued by such a court are invalid and do not take effect.
It should also be noted that in principle, it is the husband who has to work and earn a living (to provide for his family), even if he earns a lower income, and the wife should stay at home, take care of her children and tend to household affairs even if she would have earned a higher income if she had worked. This does not mean that it is impermissible for a Muslim woman to work, as long as her job is lawful, she abides by the due Islamic code of conduct in her workplace, and her husband gives her permission to work. For more benefit, please refer to Fatwa 83607.