Kraigan knows that Dahan's plans for the kingdom are not going to benefit him at all. Since Caroline has placed herself in such opposition to her cousin, I think Kraigan is sort of assuming she'd be the ruler he would prefer? Sort of the difference between someone who only might help you versus someone you know for a fact will not help you. Kraigan is hedging his bets.

(Infodump incoming): So Arkijt is mainly desert that is mostly uninhabited. The vast majority of the population lives along the southern coast, and a smaller number of people live along the borders Arkijt shares with Ceenta Vowei, Kandel, and Okkand, which is still mostly desert but more hospitable to habitation. Kraigan and his family are among these border dwellers, who have historically been ignored by the king because Arkijt's main commodities are fish and gold, both of which are concentrated along the coast. Kraigan knows this will not change under Dahan's rule. He hopes Caroline will be more attentive. Caroline's guilt comes from the fact that she actually doesn't care about the border dwellers any more than her cousin does.

Thanks for reading!