Narcissa was a very loving and supportive character toward her family. She was fully devoted to her husband and her son, not as much to other relatives. This is demonstrated in the scene where she begs Severus Snape to protect her son no matter what and when she insists on having her son at Hogwarts even though she does not like the school or its Headmaster. Just because it would mean he was close to home, and of course the final scene when she lies about Harry Potter being dead to get back to the castle and find Draco.