A family lives in a nice house, I think with her grandparents. One of the kids-a little girl begins killing people but no one knows its her. Most of the family is killed except for her and her mother. One of the last scenes involves her trying to hurt her mother with a pizza slicer.

I think you're looking for Don't go to Sleep. The pizza slicer scene is one I remember from like 30 yrs ago!
Don't go to sleep # 4 - YouTube (http://www.youtube.com/watch?v=mA0FikYR0aE)