What is the ruling on disobeying a father regarding not traveling to the Arab country where he lives alone, given that he left his family in Egypt, and this has negatively affected the physical and psychological health of his two daughters?

You are not obligated to obey your father by traveling to him if your travel would result in harm or hardship, or if your travel would be forbidden (haram), or if his command for you to travel is a matter of obstinacy. However, if your travel would not result in harm or sin, or if your remaining in Egypt would expose you to corruption and temptation (fitna), then you must obey him and respond to his command.