Politically, assuming the kingdom is more powerful than the duchy (not necessarily so), and he likes the kingdom and isn’t going to upset someone else by allying with the Future King, he’d presumably support this marriage.
But as a father, he may not like the match for his daughter. Maybe they have some other suitor in mind that they prefer, or some other reason to be against the marriage (she wants to be a celibate nun or cleric, she wants a career first, she’s a lesbian, or they just don’t like the adventurer).
Could be many reasons to possibly delay as well.
As many have said, the DM can roleplay the NPC Duke any way that makes sense to the DM.
About the younger kid who might have been a slave … Slavery doesn’t exist in most of Greyhawk, which is where the Slavers series is set. The primary lands the Slavers attack don’t have slavery. The nearest Duke is likely the Duke of Urnst.