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she was acting bratty cuz she fully believed she WAS the emperors daughter cuz she had the royal mark on her hands and i think she was jealous of ivy? i mean look at it from her prespective she had a shitty life finds out shes the emperors daughter trains so she can be proper enough to be a princess, goes to him and he basically refuses to acknowledge you and loves another girl that looks just like you plus shes a CHILD basically alot of things happened and she accidently puts everyone in danger and after it was revealed she was actually the previous emperors daughter and she goes to live with a count couple that actually loves her

I think its gonna be fine cuz the fake princess is gonna arrive AFTER the emperor adopts ivy (i think? he basically asks ivy if he could be her dad and she agrees and starts calling him that) and like lovers and prioritizes ivy over the fake princess and actually refuses to crown the fake princess as the princess
fake priness DOES go to the academy tho and shes apparently a annoying spoiled brat but she gets a redemption arc later down the story