Is it permissible for the wife to continue volunteer work that involves mixing and joking with young men on social media, despite her husband's objection, and what is the ruling on the husband threatening divorce in this situation, especially with other previous problems?

Mixing between men and non-mahram (definition) women is a door to temptation and a path to corruption. It is obligatory for the wife to obey her husband in avoiding mixing and keeping away from doubtful situations. If she does not obey him, means of reform should be followed with her progressively, from admonition to abandonment, then to non-injurious beating. If these means are not effective, divorce is the last solution.