@Countable Between all the politics and the family rankings among the nobility, a duke family is the primary pool you might consider first for marriage prospects within the country if you're a prince or princess (I'm pretty sure that's the situation with the prince's current engagement), and unless that family was actually the rare dukedom that was raised to that level for achievements and such, the head of such a family not so long ago should have been a prince or princess themselves. Just not the one that got the crown.
They might be somewhere between first cousins to slightly more distantly related, but you do this kind of thing often enough over multiple generations and that gene pool is still gonna stagnate a lot. By comparison, perhaps a bastard child might actually bring some fresh blood from outside into the royal line for once.