Will I be sinful if I divorce my disobedient wife, knowing that my son will live in difficult circumstances in her country, and I may be prevented from seeing him and providing for him?

If a wife has bad manners and is arrogant towards her husband, she is disobedient (nashiz). The husband is permitted to discipline her as stated in Islamic law: admonish her, forsake her in bed, and strike her. If she obeys, then he should not seek a way against her. If she persists in her disobedience, wise individuals from his family and her family should be appointed to reconcile them. If reconciliation is not achieved, then divorcing her is better, for the Sunnah has prohibited keeping a wife with bad manners in wedlock, as this makes the continuation of the marriage a source of corruption and harm. If a divorce occurs, custody belongs to the mother as long as she does not remarry and resides in the same country as the father. However, if either parent wishes to travel, custody is the father's right.