What is the ruling on traveling to visit family without the father if the father objects to the travel due to high costs, while the mother and children strongly desire to travel?

It is not permissible for a wife to leave or travel from her husband's home without his permission, except in cases of necessity. If it is possible to convince the husband to travel this year, that would be best. However, if he insists on postponing it until next year, then the wife must obey him and maintain ties with her relatives through phone calls and similar means.