Yeah, okay, it's a bit of a logic blunder that they haven't found her body while they have no idea what it would look like... I though wonder if some parts of the painting of her survived or not.
I don't get why some people diss the crown prince so much. He's just looking at the situation as objectively as he could - which is his duty as (future) leader, if you think about it. He clearly said here, the most important thing for him is the empire. So it's logical he would try to make a beloved former princess his ally one way or another. As long as he doesn't do that, she is a great risk to his power, even if she'd hiding and not doing anything.
Or is it that we're so focused on emotions it's become unsightly when someone tries to get by using logic? Emotions, as a ruler, are a luxury. Of course it would be nice if they meet and fall for each other, but the story is not there yet, they are not ready for that and you need to create a situation where that would be possible.
The prince's wish to make her into his ally, by marrying her, and her wish to survive, would make sure they stick together for long enough to maybe, just maybe feelings would develop.
Or is that everyone is expecting a "love at first sight"? Haaaah. Humans are so confusing.