I am also wondering the age group.  How are there parents having snacks around the children?   

There are few remedies when it comes to private schools too. 

Was how they handled food allergies, outlined and written as policies in a handbook or contract, part of why you picked the school your DD is at?

That may be the place you could turn to in order to bolster any requests you make to teachers/administration to help make your DD's situation safer. 

You paid money based on what they sold you.  If food allergy policies, or food policies, aren't outlined somewhere, or definitely aren't favorable to your comfort zone, then it is more difficult to do anything depending on the school culture and/or administration.

at first parents at my DD's school were supportive, but recently I notice parents give their kids nuts, Nutella, etc.    The parents will also eat nuts as a snack around my kid.

How can I broach this subject with the parents--  I dont want to be confrontational, but I want to say something like, "Hey, you really want those nuts, you get to clean up my kid's vomit if she's accidentally exposed"

edited to add-  I think since this is a private school, they dont have to do anything special.  Im scared they could just say, "Dont let the door hit ya on your way out"