I'm also a MB, but I can't control everything. Maybe she is going to try to replace the other nanny, and maybe she brought you in to correct some of the damage with the other nanny.
You're very new. I would focus on some fun things that you do that are special, especially for the 6-year-old, and hold the line on the snacking. They'll get with the program eventually.
My almost-6-year-old loves "activities." Call any kind of easy craft or cooking project an "activity," and he'll think you're the greatest nanny ever. Science experiments are also a big hit.
My nanny has my kids (5.5, 4, 2.5, 8 months), and she either straps the younger ones in high chairs and has everyone work at the kitchen table to facilitate these activities, or she kind of does one kid at a time while the others play nearby. She might read them all a book, for example, and then one at a time they would make the animal from the book out of construction paper (the baby doesn't make anything, obviously).