Wife avoiding her husband after being accused of committing Zina with his niece

Q: A woman disdains and detests her husband because of rumors that he has committed Zina (adultery) with his niece. She no longer wants to continue her life with him. She exerted a lot of effort to get a Talaq (divorce pronounced by a husband). When she failed, she tried to get Khul` (divorce at the request of the wife in return for compensation to the husband) but her husband did not respond to her request of Talaq or Khul`. Eventually, the wife sued her husband before the Local Shari`ah Committee, (Part No. 19; Page No. 397) which is composed of several pious scholars from the same town, and is known as the Shari`ah Court. The wife requested the committee to nullify her marriage contract. The Shari`ah Committee has exerted great efforts to get a Talaq or Khul`, but its efforts have failed. It is worth mentioning that India is not a Muslim country and does not have religious judges. This poor woman is helpless and her dignity, honor, and chastity are in danger. Moreover, she could commit suicide or become a Murtad (apostate). Furthermore, in these circumstances the woman suffers from a lack of Nafaqah (obligatory financial support), clothing, and daily needs. The Shari`ah Committee refers the case to Your Eminence to consider it and explain the ruling, keeping in mind that the Fisq (flagrant violation of Islamic law) of the husband has led the wife to disdain and detest him and to ask for the marriage to be nullified. The question is: Is it permissible in this case to nullify the marriage judicially? If the answer is yes, the Shari`ah Committee will apply it to this and will consult you as regards other similar judicial cases in the future in sha'a Allah (if Allah wills). (Part No. 19; Page No. 398) Kindly, substantiate your answer with proofs from the Qur'an and the Sunnah (whatever is reported from the Prophet).