Is it permissible, Islamically, to seek divorce due to harm caused by the husband's alcohol addiction, ill-treatment, humiliation, stinginess, lack of financial responsibility towards his wife and children, and exploitation of her money? And what is the ruling regarding child custody in this case?

There is no sin on the wife for seeking a divorce from a husband who insists on drinking alcohol, neglecting her rights and the rights of her children by failing to provide maintenance and mistreating her.

As for the custody of children, the mother has a greater right to those who have not reached the age of seven, unless she remarries. As for those who have reached the age of seven, the child's best interest is considered. If his best interest is with the mother, then she has a greater right to custody, especially if the father drinks alcohol and neglects maintenance.

It is permissible for the wife to refuse intimacy with her husband if he harms her or fails to provide the obligatory maintenance, and she may seek a divorce from him or take her case to court.