Is a traveling husband entitled to claim custody of children after a minor irrevocable divorce, knowing that he did not explicitly utter the words of divorce?

Divorce takes effect through swearing an oath to it and breaking that oath, and it is not a condition that it be in the form of "you are divorced." If the divorce is an irrevocable minor divorce (one or two pronouncements and the waiting period has ended), you are not lawful for your husband except with a new marriage contract. However, if the divorce is an irrevocable major divorce (three pronouncements), you are not lawful for him until after you marry another man and consummate the marriage with him, and then he divorces you. As for the custody of children when the father travels a permanent relocation, it necessitates consulting the Sharia (definition) court.