Is it permissible for a son to host his young friend at his mother's house in the absence of the father for two weeks monthly, despite the father's objection and even though the son is present as a "mahram," due to fear of falling into doubtful situations?

A man has the right to prevent anyone from entering his home without his permission, as evidenced by the Prophet's (PBUH) saying: "And your right over them is that they should not allow anyone whom you dislike to tread on your bedding." It is not permissible for the wife to allow anyone to enter except with the husband's permission or her knowledge of his consent. Doubt precludes permission. Obedience to him in this matter is obligatory for the wife and the son, especially given their sharing of food and drink, which might raise suspicions. If it is possible to convince him to host the son's friend while avoiding anything that might arouse suspicions, that is good; otherwise, obedience is obligatory.