What is the ruling on hosting relatives at home in the host's absence, and is it permissible for a wife to allow a non-mahram man to enter the house in her husband's absence?

Many scholars have held the view that it is not permissible for a woman to be in seclusion with non-mahram men unless there is an assurance against temptation (fitna). However, if the men are pious and honorable, and the woman is likewise, then it is permissible. This is supported by the hadith: "After this day of mine, no man shall enter upon a woman whose husband is absent, except if there is one or two men with him."

Therefore, there is no impediment to your uncle and his sons entering your house in your absence if you are confident of their honor, provided your wife adheres to the prescribed Islamic hijab and avoids sitting with them as much as possible.

As for a man and a woman entering without your consent, this is forbidden for your wife, based on the saying of the Prophet (peace be upon him): "And your right over them is that they should not allow anyone whom you dislike to tread upon your bedding."