Is she the sibling of one of your 2yr olds? I think that at age 4, she is likely bored being with 2yr olds all day. She needs a group of kids her age that will socially stimulate her and provide more appropriate company. The above behaviors may all be just poor behaviors learned at home...but they are quite possibly due to boredom.

If you are able to lose the income and easily fill the spot I would have the family find a daycare for her that has some friends her age. If you want/need to keep her on it will take a lot of effort on your part to tackle every single behavior as well as ensuring that she is stimulated and challenged within the daycare.