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basically, the other person who've helped the mage to perform the time return magic was the grand duke because the moment keira died, the spirits went on chaos, thus, confirming that keira is the legit daughter and the spirit user. so they fucked up and did that magic to change what would happen in the near future. also, this ain't romance, making the ml non-existent (but some novel readers told that this manhwa doesn't follow the flow completely in accordance to the novel, so the ending might change and romance might exist???)
if you want to know about cosette(?) she is indeed legit. however, only the body and the blood, for the real cosette is dead and her body was possessed by a demon or smth like that. making keira the legitimate spirit user.
in the novel's ending, keira and her younger brother cutted off their ties to the grand duke and left the grand duchy (satisfying, isn't it?) but like what i've said before, the ending might change :((
that basically sums it up. if you want detailed and more spoilers, just search for it on the net (づ ̄ ³ ̄)づ

omg im so sorry but i dont know the details honestly,,, i've just read a spoiler forum for the manhwa. but i guess it's because the grand duke is an idiot. i mean, he was a dick and it would be reasonable for the siblings to leave him. and basing on keira's actions, she basically doesn't give a fuck about her dad now. yeah, the present has change ngl but if we put ourselves into her shoes, wouldn't we be greatly traumatized? with all those humiliations, degrading she had experienced, and everyone turning their backs on her (excluding her brother and the knights) and of course, the fear of getting killed and dying when you know that you did nothing wrong. man, i'd be scared and get traumatized for all of those shits that happened to her :((. i can pretty much understand why did she chose to cut off her ties with the duke
Drop some spoilers pweaseee