Is it permissible for a woman to seek divorce from her husband who repeatedly leaves the marital home and demands money in exchange for divorce, and can she divorce herself from him Islamically, given the existence of an Australian divorce paper and the marriage being documented in Lebanon?

A man's kindness to his family is proof of his noble character. Allah Almighty has commanded the husband to treat his wife with kindness or to release her with grace. The Quran called holding onto a wife with the intention of harming her an injustice (dhulm). The husband must fear Allah and treat his wife and children well, and bear the responsibility of providing for them. The wife can refer her case to an Islamic center or any other authority that can relieve her of harm if the husband insists on hurting her and depriving her of her rights.