That is exactly the kind of emotional manipulation I was referring to in the thread about what kind of provider you are. I am very no nonsense and don't tolerate that kind of thing well either. It doesn't take the kids long to figure out that they cannot manipulate me the way they can their parents.
What I would do OP in your shoes, is not give her any kind of clue or sign that it is rest time. Don't announce that its rest time at all. Don't allow her the opportunity to follow you around and build up to being sad and screaming/crying.
Put her down first before everyone else. Swiftly and quickly. If she fusses. Let her. Don't give her any attention for it.
I am guessing she will figure out really fast that you aren't bothered by her antics and that nap time will come any ways no matter how much she protests.