Is it permissible to divorce an abusive wife who refuses discipline, and is she entitled to child custody in a turbulent country, especially since the husband fears for them due to her behavior and the circumstances of his country?

The wife is commanded to treat her husband kindly. If she acts superior to him and insults him, she is considered disobedient (nashizah) and deserves discipline. If that does not help, then divorcing her is recommended. However, since there is a child, do not rush into divorce. Instead, strive to reform her, pray for her well-being, and involve wise people from your family and her family, acting upon the Almighty's saying: "And if you fear dissension between the two, send an arbitrator from his people and an arbitrator from her people. If they both desire reconciliation, Allah will cause agreement between them. Indeed, Allah is ever Knowing and Acquainted [with all things]." If reconciliation is not achieved and cohabitation becomes impossible, and the benefit of divorce outweighs other considerations, then resorting to it is preferable.

In the event of separation, the mother has a greater right to custody of her children unless she remarries or there is an impediment affecting her eligibility. If she wishes to travel, the father has a greater right to custody of the children according to some scholars, and the child's best interest is the determining factor in custody. If a dispute arises, it is best to refer the matter to the Sharia (definition) court.