Looking for the Villainess's Contract Husband

One day, a young girl realizes she has been reincarnated as the daughter of a villainess in a novel. Thanks to her memories of the original story, she knows the future, but it is far from hopeful: her mother is destined to be used and killed, while she herself will die from an incurable illness. Even if she cannot save herself, she decides to save her mother. To change their fate, she makes a deal with a duke from the original story and asks him to marry her mother. After escaping her cruel grandfather’s control, she plans to quietly face her own death—but a suspiciously sickly young boy suddenly starts clinging to her.