This emperor pmo. like I get that the empress is evil but how can he expect to take care o...

While normally I'd agree, this is a medical setting. It was quite common for emperors/kings/etc. to have more than one wife at the same time. In fact it was expected, and they could lose favor(in some regions) for not.
It was especially common if the empress was mostly a political one

that sort of thing is normal is this setting though. The fact that he has a kid from another woman wouldn’t be any reason for her to be upset, seeing as it’s normal. And since her kid is the heir, there’s no succession problems either. Also it’s not like shes in love with the emperor, they got married for political reasons. I’m pretty sure their son was even ‘conceived using magic’ so they never even had sex.

Even if all that is true he can’t expect her to take care of someone else’s daughter like its her own kid. And she seems to have a grudge against fl’s mom and maybe she did actually develop feelings for emperor despite the marriage being a political one. I think you shouldn’t assume stuff just because having multiple wives is “normal” in this setting. In my country its also still normal to have more than one wife but that doesn’t mean they’re gonna be happy about it, bc ik they all wanna be “special” or the davorite wife

did the emporer make her take care of his daughter? I thought she did that on her own because she wanted her to trust her?

The empress did take care of her, out of her own will, she asked the emperor to have permission to take of the princess.

The emperor agreed.

And she would pretend to care for the princess, but she was just making the princess her doll that she could control.

I’m asking
Do you want spoiler about MC mother?

Sure

Spoiler
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FL father and mother were engaged and lovers before the duke house killed the FL uncle and grandfather.
(The emperor was the second prince without any desire to the throne)
Because the empire was in such a mess the father needed the duke house support and was put into position of marriage with the duke daughter, aka the empress
He was forced into this marriage to avoid the falling of the empire

The third person in this relationship is the empress, not FL mother since FL mother was there first.
Emperor never promised the empress love, it was a contract marriage. Even FL brother was made with magic; emperor gave empress lots of power and never shaken her position (until he learned that she abused his second child)

Also, empress never loved the emperor. She loved her position of power and FL being born shaken it
There is no excuse for the way the empress abused a child and framed her throughout her childhood
Even if it was an heartbreak (which it wasn’t) that lead to her to act like that, there is a difference between “not being nice” and the abuse FL suffered her first life.
No excuse for that.