Is it obligatory to fulfill the condition set by the wife's father that his daughter not travel outside her country, knowing that she reluctantly agreed, and given that the couple is being harmed by remaining in this country due to racism and receiving death threats?

There is no harm in a husband traveling with his wife to another country, especially if she consents, and this is for several reasons:

Firstly: If the couple's remaining in the country threatens their lives or causes them significant harm, then the condition preventing the relocation of the wife from her country loses its utility, because its purpose is the wife's benefit. If it turns into harm, then it is no longer valid.

Secondly: Although the condition of not traveling with the wife is valid, fulfilling it is commendable (mustahabb) and not obligatory, in the opinion of the majority of scholars. As Al-Buhuti mentioned in Kashshaf al-Qina': "And fulfilling it – meaning the valid condition – is not obligatory; rather, fulfilling it is sunnah."

Thirdly: The validity of the condition means that the wife has the option. If she chooses to travel with her husband, she thereby waives her right, and there is no harm. Al-Buhuti reported that Umar ibn al-Khattab, may Allah be pleased with him, said in a similar incident: "She has her condition," and he also said: "Rights are settled upon conditions."

Therefore, there is no harm for the couple in leaving the country and traveling to another country where they can be safe themselves and their children.