Would the only son's travel abroad for work—despite his father's refusal and his mother's approval—be considered an act of disobedience (ʿuqūq) and a loss of blessing in his sustenance, knowing that the father does not need his son, and the travel would improve the family's standard of living?

If travel is safe, the father's permission is not required for travel for trade or similar purposes, and the son is not considered disobedient for disagreeing with his father in this matter. Nevertheless, it is recommended to strive to convince the father and gain his رضا (satisfaction). If the father insists on refusal and there is no harm to the son in abandoning the travel, then it is more virtuous to abandon it as a sign of filial piety towards the father; because honoring one's parents is among the best acts of drawing closer to Allah.