The MC does not have a blood claim to either. Remember he would marry into there royal lines. Greatly weakening his position geo-politicaly. There is also the factor the citizens of both realms would hate this, most of all the fey. There cultures are to alien to each other.
I can understand peace comming about because the heirs of these nations being half siblings. Thus not wanted to have bloodshed of there sibling. While the MC and his children live I can see peace being maintained, well after the crisis event is over.
Going by Sam's testimony I believe the crisis is a return of demons. I also fully expect the princess to be possesed by one.
To be fair, we don't really know a lot of about the MC, other than he is missing a lot of his own background, even after you find out sis's big secret. While the Fae are far more liberated, it has been shown that the humans are still pretty sexist, so if you marry the princess, even if you are a commoner, you would be the one in charge by token of gender.
Hard to say about the demon invasion, not enough evidence, though if so, it's hard to say how killing half of the elves and all of the humans would save them from that invasion. Though I do have to agree, that the princess seems possessed. Or possibly just a split personality, but that seems less likely based on the crone. And since I still think the crone is likely the long lost princess, and she clearly knows more than we do, her version seems one of the more accurate.
We are half Fae, and of the Queen's blood, so we have a reasonable claim to be her new husband, and as the king of the human lands, he can bring them all together for a peace, love, dope summit, but this depends on the other threat, be it demon invasion, drought, meteor, whatever.
