Concerning divorce: Chinese society was very patriarchal, but it also had complex rules of propriety and hierarchy. As a civil official, thus a Confucian scholar, Dad was particularly bound with rules of propriety, as enforced by censors. I guess that military officials would have more latitude, princes yet more, and emperor could at worse be admonished by the censor, sometimes with fatal consequences to the censor. Wife could not initiate the divorce, period.
Demoting or divorcing the main wife had to have one of the listed reasons, including jealousy toward a concubine, but a "perfectly legitimate request" would not count as jealousy.
Clearly, MC wants to provoke the concubine (sorry for not looking up the name) to commit a provable crime.