Is it permissible to travel or marry another girl while the father is angry after his son became agitated with him and refused to marry his cousin?

The right of a father is great, and one must repent to Allah for any statement that angers him. Obedience to the father is not obligatory in marrying someone the son does not desire, and this is not considered disobedience; for a long marital life requires acceptance and desire. If the paternal cousin is righteous and the young man desires her, that is better, otherwise there is no harm in leaving her. There is no harm in traveling despite the father's anger after apologizing, and one should continuously strive to appease him, show him dutifulness, and treat him kindly through communication and correspondence.