How can one deal with a young man from the husband's family who has misbehaved, while preserving family relations and avoiding marital and family problems?

The joking of a young woman with non-mahram men is forbidden because it leads to fitnah (temptation/strife) and speaking in a soft, alluring manner. Some scholars have explicitly stated that the laughing of a non-mahram woman with a non-mahram man is forbidden and warrants disciplinary action (ta'zeer). Therefore, the sister must repent from joking with these non-mahram young men, and be wary of mixing with non-mahram men and speaking with them, except in matters approved by the strictures of Islamic law.