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.
It is not permissible for a Muslim to initiate a case in a court that does not abide by Islam (the Islamic Law) in judging as we clarified in Fataawa 86134 and 88749. However, if a Muslim is obliged to resort to such courts, then this is permissible.
Undoubtedly, a Muslim is not permitted to divulge the secrets of marital life, especially what pertains to the matter of bed (i.e. sexual intercourse). Abu Sa’eed Al-Khudri narrated that the Prophet said: "The most wicked among the people in the Sight of Allaah on The Day of Judgment is the man who shares intimacy with his wife and she with him, and then he divulges her secret." [Muslim]
However, if a person is obliged to mention some of this, it becomes permissible for him to do so but according to the necessity only, and if he can repel this necessity by indirect reference then it is not permissible for him to speak about it explicitly.
Moreover, this woman has no right to ask you for monetary compensation because of you being negligent with her about her right in bed. If the court rules that you have to pay any compensation, you are not obliged to pay it and you should find any trick to avoid paying it.
Moreover, it should be mentioned that a Muslim who resides in a non-Muslim country may find himself in such difficulty. It is for this reason that whenever a Muslim can migrate to a Muslim country, then he should do so; for more benefit, please refer to Fatwa 86405.
It should also be noted that it is not permissible for a Muslim to marry a non-Muslim woman except if she is among the People of the Book and she is chaste. Rather, it is more appropriate for him not to marry a woman of the People of the Book especially at this present time because such marriage may lead to disadvantages, some of which are mentioned in Fataawa 88451 and 84724.
Allaah Knows best.