Four is an age when they can be bloody difficult when they want to. They are testing the limits of what they can do and what power they have over everyday decisions. Plus ANY attention is better than none to them. If her parents can manage it, maybe they could ignore the bad behaviour and not "reward" it by getting worked up?
Easier said than done, but it is possible. nursery and admission class teachers do it all the time, saving their energy for the unavoidable battles. You can't fight twenty of them at the same time.
Suggest they try not to openly "ask" her to do something, then there is nothing to refuse to do - sneak it up on her. The old "choice" trick often works, like asking, "Which coat are you wearing today?", instead of "Put your coat on!" and if she say "None!" when it is brass-monkey freezing outside, say "OK, I'll put it the car then, in case it is colder later." and then DON'T MENTION IT AGAIN, just put on their own (parent's) coat and carry hers out to the car. Fight averted. She hasn't "won" because there wasn't a battle to win.
She may get a bit cold, but that is the natural consequence of not wearing the coat, and she will learn from experience that it is not pleasant. She may even have the coat on by the time the car arrives at the destination, with no asking at all.
DO NOT then say "I told you so!", just hand it over casually If they are walking, then carry the coat (without any more comments) until she wants to put it on.
They may need to get inventive - the same trick may not work twice running - but by not letting their blood pressure go through the roof over it, they make it unimportant, and not worth her making an issue of it.