Is a promise of divorce considered a divorce, and is a wife considered disobedient (nashiz) if she abandons the marital home and refuses to renew the residency permits of her husband and children, and who has the right to custody of the children? What are her legitimate rights if a divorce subsequently occurs?

The phrase you uttered is merely a promise of divorce, which does not constitute a divorce, nor is it binding to fulfill. Your wife remains under your marital bond. It is her duty to obey you by returning to your country, and her refusal to return constitutes 'nushuz' (disobedience). The custody of the children belongs to you unless your wife returns to your country. We advise you to strive to reconcile with your wife and to involve relatives for this purpose. If she persists in her 'nushuz', you may pressure her to relinquish some or all of her rights before divorce.