From what I heard
Kinda spoilers? Again I could be WRONG
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Apparently Emperor was obsessed with a woman who had white hair & green eyes?
And i think he's directly responsible for Olivia's birth? Forcing the Duke & Olivia's mother to have sexual relations
From what I remember, the Emperor hated that Olivia’s so called father and the Duchess had a perfect relationship in society. So to tear them up, he purposefully drugged Olivia’s mother and father and had them sleep together to tarnish his reputation. Her mother was presumably blackmailed or coerced and she was a victim herself.
But from what I’m guessing the reason for the engagement stems from having the Crown Prince married to a woman from a high ranking family which the Madeline’s are in society. If not for Olivia, then the engagement would be pushed onto her younger sister but everyone knows the Prince has a lover of his own.
Meanwhile the Emperor wanted his daughter to marry the Grand Duke and rule there.
So what's the deal with the royalty here? Why are they adamant to keep the engagement with her?