Forgotten Title Isekai KR novel with female MC where she changes villain but both die and she goes to past...

Hi there was this promo Manhua i found once that drawn my attention to a KR novel where the Female MC gets reincarnated in a novel world she read and she ends up serving the villain prince, originally she changes him for the better but because of that they are betrayed and die tragically or something along those lines, when she died she went back to the past and now she wants him to become a proper tyrant, which with her knowledge of the novel will be able to win the fight for the throne and survive, well something along those lines, does anyone know the title of this work ?

I also remberered another detail, she reincarnated into a character that was brought originally to him when he was young to poison him using her family as hostages (but since she read the novel she knew that the familly was already dead so she did her own thing).

Lastly this one i'm not sure of, because i may confuse it with something else but i think i remember the cover art being something along the lines of her (with brown hair and tied up hair) holding on to the villain who is dead on her lap, she was looking upward in that image.