I think the Duke and Camilla are calm because Rania is too sus. She showed herself at the birthday party, no previous contact or even a letter of intention. She made it very public. Even if they don't speak of it, those hints live in their subconscious.
The bracelet was also a precious gift meant to commemorate Ludvig's birth, it's not the type of gift that one gives away to a daughter to wear. It would be more believable to use it as a token of proof, not wear it.
Her son is a better person than the mother. He has the maturity to manage the orphanage and hopefully his own personal life. He won't pretend to be a saint and cause so much pain to her own child.
She's dead now, so basically he's gone no contact with her. Her memento just gave him a moment to realize she had never forgotten him. But that's just the author's fallacy, she probably kept many boxes, she even forgot she had this box.
I hope out dragon gets to save the people she wants. Change irl is hard enough, at least I can live vicariously through novels.