What is the ruling regarding a house that my wife’s parents gifted to her, given the existence of the sons of her maternal uncle who died before his mother, who gifted the house to my wife’s father? And is my wife obligated to apply Islamic law to what was gifted to her?

If the house transferred to her father through a means they believe to be permissible, then the house belongs to her father, and this is affirmed even if he converts to Islam. This is based on the statement of Shaykh al-Islam Ibn Taymiyyah: "If a disbeliever deals with another disbeliever using usury, and then they both convert to Islam after the قبض (receipt/possession), and they seek our judgment, then what he has taken possession of is ruled to be his, just like all other things disbelievers possess through contracts they believe to be lawful. For example, if he sold wine and received its price, then converted to Islam, that becomes permissible for him, as the Prophet, peace and blessings be upon him, said: 'Whoever embraces Islam upon something, it is his.'"

If it is affirmed for him, then he is permitted to gift it to his daughter, and she is permitted to accept it.

However, if the house transferred to him through a means they believe to be forbidden, then the house does not belong to him, because it is not from their religion. Therefore, his daughter should not accept it if he gifts it to her.