What is the ruling on a husband swearing to divorce his wife if her family interferes in the matter of her returning to him, and does the divorce occur with this oath that was issued out of anger and psychological pressure, and is expiation required of him?

If you swore by Allah that you would divorce your wife if her family interfered in a specific matter, and then you broke your oath due to their interference, the divorce does not occur. This is because you did not make the divorce conditional on this matter; rather, you merely promised it. You are obligated to offer expiation for breaking an oath (kaffarat yamin). A promise of divorce does not take effect, nor is it obligatory or even recommended to fulfill it.