A Marauder's Daughter

At age seven Hermione was told to run by her mother, to run and not look back. Being who she is, she followed those directions to a T. Only she got lost in the woods on the night of a full moon. What happens when Remus finds her and doesn't kill her? What would her life be like if she were raised by a Marauder? How would it change her years at Hogwarts? HR is a 4th year by chpt. 5