Is the husband obligated to obey his mother and divorce his wife, knowing that she is the second wife, out of fear of violating custom and not because of any wrongdoing on the wife's part?

A mother does not have the right to order her son to divorce his wife, especially if the reason for the order contradicts the Sharia of Allah. The son is not obligated to obey his mother in divorcing his wife, as this is not an act of birr (filial piety). The husband should honor his mother and treat her well without divorcing his wife. The mother should be advised of the necessity of adhering to the Sharia, and the wife should strive to treat her husband's mother kindly and win her affection.