@Binary10011 from what I understood Artezia is the daughter of the Rozan Marquess and Mireila (is that how you write it?)
Adultery is frowned in this world so the emperor brought Mireila and placed her as the Marchioness to keep her close in a not so obvious way (though everyone knows, so it's just for appearances)
Then they had a son, and later Mireila had Artezia with the Marquess.
I wonder if the emperor just didn't care his lover had a daughter with another man because it was part of the deal (the Marquess would need an heir as well) or because he doesn't really care for Mireila all much, though this would be weird considering he still visits her, so I'm inclined to the first option.
That would explain a bit of Mireila's character, being placed in a fake marriage because she couldn't marry the king, have his son who couldn't be immediately celebrated as the crown prince, then having to give birth to a child for her fake marriage for appearances' sake or duty.
It wouldn't be strange if she loved/hated Artezia because of that (maternal love vs hate for the Rozan bloodline) and would explain better why she had no issue with poisoning the Rozan family.