Is the questioner considered disobedient to his parents, and what should he do to please them after his father disowned him and his mother asked him to travel to improve their living conditions?

The outward appearance of a father's anger and his disownment of his son due to his travel has no legal justification in Islamic law. A father does not have the right to prevent his son from traveling for his own benefit if the travel is safe, and this is not considered an act of disobedience (disrespect to parents). The son must communicate with his father, treat him with kindness, and pray for him to gain his رضا (رضا). If the parents differ on a matter, the son must strive to reconcile between them, as Imam Malik said to someone who wanted to travel to his father while his mother was preventing him: "Obey your father and do not disobey your mother," meaning to go to great lengths to please his mother until she agrees to his travel. Efforts must be made to reconcile between the parents, and a father's disownment of his son by denying his lineage is a grave evil.