Well, this is what I think may happen:
1. Since her dad is suppose to be the executioner, the king is going to the duke's house to see it go through.
2. The duke is going to refuse, the duchess is going to plead with the king, and everyone will try to dissuade the king including the two MLs.
3. At some point of time, she'll be in danger, but no one will be able to come to her aid except for the castle itself.
4. They'll realize how important she is and that she can't possibly be executed now.