I dropped this for a while, can someone summarize why she's back at the shithole?

That shitty adoptive father made a claim that she is his daughter so the emperor allowed him to take her

i need that little sweet prince to take over the trone cuz the only prince i can trust to protect hailyn in that freamin emperial house

What- and there was no fight or evidence of some sort?

There was a whole scene about proving she's the Duke's child via some magic potion thing. Someone manipulated the potion, so during the ceremony it showed that mc wasn't related to the Duke, forcing her to go back to her adoptive piece of trash.