Is a husband entitled to prevent his wife from spending the night at her parents' house or traveling with her family due to the presence of an unmarried male relative there, and is his feeling of jealousy and discomfort considered a legitimate justification for that?

First: The presence of a non-mahram woman in her father's house with a non-mahram man is permissible if there is no fear of temptation (fitna) or unlawful mixing. If there is fear of that, or if she does not adhere to the legal hijab, then it is not permissible.

Second: If your wife's father and brothers are lenient about the presence of that non-mahram man with your wife, then it is not permissible for you to leave her with them. You must protect your wife and not expose her to temptations.

Third: Your going out for recreation is permissible as long as the place is not one where people of immorality gather. If you fear the presence of the non-mahram man as a cause of temptation, then you must prevent your wife from traveling with them.