Is it permissible to seek a khul‘ (divorce initiated by the wife) from a husband who does not care for his wife and daughter, treats them badly, does not spend on them, has illicit relations, drinks alcohol, and forced his wife to engage in anal intercourse?

Anal intercourse with a woman is forbidden by the Qur'an and Sunnah (definition), and it is among the major sins. A wife is not permitted to enable her husband to do this, and she has the right to seek divorce if he does not desist. Sheikh al-Islam Ibn Taymiyyah issued a fatwa (definition) stating that anal intercourse is forbidden by the consensus of the general body of Muslims, and that "the tilth" refers to the vagina, not the anus. This act is of the same nature as sodomy and necessitates punishment for those who commit it, and it may even require separation between them.

As for the husband's ill-treatment, his drinking alcohol, and his illicit relationships, these are valid excuses that permit the wife to seek divorce. The "bās" (distress/hardship) mentioned in the Hadith (definition) ("Any woman who asks her husband for divorce without any bās...") refers to the compelling reason for divorce, such as ill-treatment, the man's immorality, and his deviation. It is advisable to seek divorce if the husband persists in his state. If the judge refuses to grant her a divorce, she should then seek khul' (divorce by mutual agreement, usually with compensation from the wife).