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 is His slave and Messenger.
If your wife asks for a divorce or for the invalidation of the marriage without a sound reason, then she is sinful. For more benefit in this regard, please refer to Fatwa 88408.
So, you are not obliged to accept her demand but if she hates staying with you and fears to be neglectful about your rights, then she has the right to ask for Khul’ (divorce upon the request of the woman) in return for compensation which she pays you. For more benefit, please refer to Fatwa 89039.
As regards the judge whom you mentioned in the question, if he rules by man-made laws, then it is not permissible in principle to take the case to him. If he rules divorce or Khul’ or invalidates the marriage according to these laws, then his ruling is of no value and it should not be taken into account.
Finally, it should be noted that if there is no Muslim judge, then the Muslims should take their case to Islamic Institutions and Centers. A Muslim judge is supposed to rule only according to the Sharee’ah (Islamic law).
Allaah Knows best.