I have thought about the historical cases of kings having more than one kingdom and how this should be modeled. In the English case, the important titles for long after the Norman conquest were not the kingdom of England but the Duchy of Normandy, the County of Anjou and so forth. Henry II appointed his sons to govern the disparate territories of his "empire" (and using disinheritance as a constant threat against disloyalty) and later the Prince of Wales gained some authority as regent over the Welsh principalities, as also the Lord Lieutenant of Ireland did in his jurisdiction.
There are similar instances of appointing trusted men or family members to rule over lands distant from the monarch himself. Aragon employed viceroys rather early in their Mediterranean empire, and the Habsburgs later built on this model, appointing in the sixteenth century viceroys in the Netherlands and in the Americas. But the idea was medieval in origin, someone who held the place of the king (the literal meaning of "lieutenant") and received many of the same dignities as the monarch himself.
So to my question, should there not be a way to appoint lieutenants or viceroys over your secondary kingdoms? In my way of thinking this would not be mandatory, but it should improve relations with your vassals in that kingdom (provided the choice of viceroy is worthwhile) at the expense of losing some control and revenue. There could be certain rules, such as requiring that the kingdom to receive a viceroy not be contiguous with the primary kingdom or that the center of the secondary kingdom be a certain distance from the capital, to cover cases like Wales for England.