I think it's important to consider the family dynamics as well. Obviously, the mother is out of the picture, because of a lethal accident, or because of a hostile divorce, but anyway, this little girl has lost her mother in a traumatic way and probably feels very alone in the world.

Her father is playing family with a new wife and presumably tries to divide his attention between his daughter, the child of his new wife, and his wife. This volatile balance is threatened by the arrival of a new baby, the only child in the house that will be living with its father AND mother, and the seal on the new bond of the couple. This will definitely further reduce the time and love the six-year old will receive.

I don't really think that stickers and food rewards will address this existential anxiety or relieve the girl's nightmares and fears of abandonment... All too often, sleep issues are just symptoms of much deeper-rooted problems, and it's important to address them.