Is it permissible for my brother to marry a second wife without his wife's knowledge, or to divorce her without paying the deferred dowry of 10,000 Kuwaiti dinars, given her bad conduct and her saying, "Shit on you and on the Quran"?

A woman who utters words of disbelief (kufr) and abandons prayer, in addition to her disobedience (nushuz) and poor treatment of her husband, has apostatized from Islam. It is not permissible to remain married to her because the apostasy of one spouse necessitates separation. Scholars differ on whether the separation occurs immediately or is contingent upon the expiry of the 'iddah (waiting period). If she returns to Islam within the 'iddah, her marriage remains valid. The deferred dowry (mu'akhkhar al-sadaq) is not nullified by apostasy and remains a debt owed by him. He has the right to refuse to divorce her until she relinquishes her claim to the'mu'akhkhar al-sadaq if she persists in her disobedience.