What is the Sharʿī ruling regarding two brothers traveling to work abroad, while their parents are over sixty and serving them, and is there any advice for the children?

If the travel of the two brothers causes no harm to them or to their parents, and they are certain that their parents will not be neglected in their absence, then there is no objection to their travel, even without the parents' permission. Traveling with their consent and permission is better. For whoever prefers to stay with their parents to be dutiful to them, that is a tremendous door to good. The advice for everyone is to be keen on honoring one's parents, for they are two doors to Paradise. The means of honoring them are many, so whoever cannot stay with them should make sure to call them, assist them, give them gifts, and bring joy to them.