I think that the daughter was pregnant, things went wrong while giving birth, and after she delivered, she died. The mother, meanwhile, was unable to deal with losing her daughter, and so she ignores the newborn daughter and tries to bring her daughter back to life, praying that it will work.
I don't think Sophia actually offered to grant anything: it sounds more like she told the mother instead to offer herself as a physical vessel for Sophia--like Ysayle did with Shiva--and that was ease her pain.
Now if that's right... what happened to the child?