I read it that she was his daughter, he didn't cheat on the Empress, they got a political marriage and they respect each other.
As the Emperor he has the right to have other "concubines/queens" and he did that with the FL mother, which who he truly loved.
The Empress knew and respected his choice and she'll still love the FL and treat her as her own child. (That what I read)
Political marriages were common in the time period that this is based on. Even more so in cultures that allowed multiple wives/consorts. It was considered natural to love your own children more sure, but it wasn't uncommon to love the children mothered by another as you would likely have a hand in raising them too.
I don't think the emperor loved her mother. Even her mother said to her that even tho the emperor didn't love her, he is still very kind. I think the emperor isjust really kind in nature. Then about the empress, I read spoiler when they said she will treat the mc just like how she treats her own daughter. She is also kind. The empress and emperor doesn't love each other, it's just a political marriage but both shared trust and respect with each other.
Its possible that the mother just thought the emperor didn't love her back when he did? Regardless tho my concern is more on how she died. It was explained that her clan descended from a god that would curse them to be forgotten (and therefore die because they live thru memories) if they had a child with someone outside of the clan. This is likely because the child's existence wouldn't depend on the clan's weakness of living through others' memories and the clan could technically try to leave the god's influence by having children with only outsiders.
If that's the case tho, why wouldn't the emperor have enough people in the castle so that when the child was born, there would be someone around to recognize that there is a child there when their memories eventually disappeared upon her mother's death? Upon first glance anyone would be able to tell that she is the child of the emperor. Regardless of whether or not he felt nothing or there was a misunderstanding and he really loved her, he was mature and attentive enough that he made sure she had every comfort she needed, so what kept him (or the people he sent) away?
I think it's between the sentence where it said about the emperor brought a woman in the palace but since she was sensitive to sound they made a place for her which is far from noise. Maybe it's because that place is intended for her that it became storage when she was forgotten. I mean they also forgot what that place was for and became storage.
I hope Estrella is not his child. Dont get me wrong, I want estrella to be a part of their family. Its just that the king is so good that I would love it if he didnt cheat on the empress. And the empress seems like she will be a good mother to estrella.