I worked as a behavioral therapist before this, and I'd take being spit on over screaming.
The key is consistency, and getting parents on board. If you have an extra płaypen, I'd set that up somewhere not within the direct line of sight of the playroom or wherever she does it the most (but where you can still discreetly monitor her). When it starts up, take her there immediately, without giving her any attention, even eye contact. Try to get the other kids to ignore her as well, not even to look. Like others have said, when she finishes take her out, tell her "you can ask nicely to get the toy" or whatever she was screaming about. Avoid saying "don't scream" instead, give her a behavior to replace the screaming with. Try to engage her to show her what appropriate behavior gets. And when she screams again start all over. Eventually she'll realize that screaming not only doesn't get her what she was after, it doesn't get her attention either. It could be that the screaming started with her not getting toys, but if she's noticed that it gets her attention and she might be after that now.
Remember that it will get worse before it gets better! When she first realizes that it's not working, she'll escalate to see if that works instead. Be firm and consistent! Encourage the parents to do the same, it'll make the process so much shorter and smoother for you.
Good luck! I hope this helps!