Is the husband obligated to fulfill his promise to his wife and buy the agreed-upon gold first, or to send his parents for 'Umrah, knowing that his father is well-off and has performed Hajj before?

The dowry is a rightful and obligatory entitlement for the woman from the man. Whatever remains of it is a debt upon him that must be paid, unless the woman willingly relinquishes it. If the due date for paying the dowry arrives, the husband must prioritize its payment over sending his parents for Umrah (definition), if he cannot do both. This is because settling a debt is obligatory, whereas sending parents for Umrah is supererogatory. If the due date has not arrived, the woman does not have the right to demand it, and mutual understanding and forgiveness between the spouses are advised.