Is it permissible to have a legitimate Islamic marriage without officially registering it in court to avoid residency issues and the disapproval of children, while maintaining a lawful relationship?

For a marriage to be valid, official procedures or court documentation are not prerequisites. Rather, it becomes valid upon the fulfillment of its conditions: the guardian (wali), two witnesses, and the dowry (mahr). Marriage is not valid without the permission of the woman's guardians. If her guardians are her sons and they refuse, then it is not permissible. However, if her father is alive, he can marry her off. The woman can mediate through her relatives to convince her sons to agree to the marriage, provided that there is a commitment not to register it in court.