Use the adjective faux-naif to describe behavior that pretends to be innocent or childlike. Your sister gets away with everything, because her faux-naif act (chin trembling and eyes filling with tears) always works on your parents.
When someone is faux-naif, they're putting on a shrewd charade, pretending to be innocent or simple — actually, they know exactly what they're doing. A faux-naif bully might stick out a leg, tripping your friend, then say, "Gee whiz, sorry about that, I didn't know my leg was in your way!" In French, faux-naïf means "false naive" — naive has a Latin root meaning "natural."