Callytrix didn't live with the Dursleys she left when she was 13 years old. She was brought by her friends who are purebloods from Korea who had decided to adopt her into the family. The Peverell family found out that her magic was blocked they weren't very happy about it as they are the descendant of Cadmus while Callytrix is Ignotus's descendant. As for the mother of Callytrix she was a childhood friend to the mother of her friends. That was until she reaches 14 and had to go back to hogwarts where danger just leads her to another one.