How can a husband deal with his wife who persists in behaviors that arouse suspicion and jealousy, such as being lenient in her dealings with her cousin's son and him touching her, and her accompanying her aunt's husband and speaking with him secretly, despite his repeated warnings, seeking to please God and then himself?

What you have mentioned about your wife's negligence and dereliction in her dealings with her cousin, such as appearing before him in house clothes, joking with him, and him touching her, as well as her calling her aunt's husband—all of this is a clear abomination and a pretext for falling into immoral acts. It is not permissible to be lenient about it, and you must prevent her from it, in accordance with your guardianship.