Big Spoiler
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the emperor didn't want to marry the empress, she said she had no feelings for him and that would be a political benefit and since he was already with the mother of the female lead, but he couldn't marry her because she didn't have a high noble status , he accepted the offer. At the beginning the Empress was also nice to the mother of the female protagonist and the Emperor thought they could become good friends. One evening the Empress mixed alcohol into his medicine. When the Emperor woke up the next day, he was lying in bed next to the Empress and she told him that they had slept together. Shortly afterwards she said that she was pregnant.
He was devastated because he fought he cheated on the family Mother.
The girl with red hair is not his daughter. He is suspicious about it. That’s why he does not like her that much.
the real villain is the dad because not only does he discriminate base on blood (e.g. not loving the red haired girl js bc shes from a consort which isnt even her fault btw??) but he js pushes his desires onto other people e.g. he never once asked shushu if she wants to live with him and js assumed that the duke sucks and doesnt love shushu. hope shushu doesnt go back to him cuz he highkey sucks !!!