What is the legal ruling for this situation, and what is the appropriate way to end this problem?

The father erred by insulting the wife's father in front of her, for insulting a Muslim is a transgression (fusuq). It is forbidden to insult a disbeliever if insulting him leads to harming a Muslim, so what about insulting a Muslim? It would have been better for the wife to suppress her anger, but her reaction did not exceed what the father did. The father and mother should reconcile with the wife, because boycotting a Muslim for more than three days is forbidden in Islamic law. "Whoever boycotts his brother for more than three days and dies, enters the Hellfire." And "whoever boycotts his brother for a year is like shedding his blood." Ask your parents to reconcile with your wife, out of consideration for God's right and for the sake of your young children. And encourage your wife to maintain ties with her husband's parents and to appease them.