Looking for the Villainess' Contract Husband

One day, while suffering from a fever, I realized that I had been reincarnated as the daughter of the villainess in a novel. Thanks to recalling the original story, I became aware of the future, but it wasn’t exactly hopeful. My mother, the villainess, would be used by others until her death, and I was destined to die from an incurable illness. Still, there was one good thing. Though there was no way for me to survive, I could save my poor mother. Mom, you’ll live. Instead of me, live happily. To save my mother, I went to find the duke who was a supporting character in the original story. So please propose to my mother, Your Grace. Knowing the original story, I made a deal with him, and in return, the duke rescued my mother and me from the clutches of my cruel maternal grandfather