She's furious that the school isn't taking action to mitigate the risk to her daughter so that she feels safer. I don't understand why your response to that is to say the OP is being hysterical!
As a parent with a child with multiple acute allergies, no one can make the child feel “safer” education and the child managing there allergies is the safe and only way to ensure she is safe and I even safe that with difficulty, there is no “safe” when it comes to allergies, it’s a false and wrong sense of security.
This child could be at the cinema and someone is eating peanut m&m in the theatre, the child could be on holiday and sat next to someone eating chicken sat-say, the child could be waiting at traffic lights and someone is eating a snicker bar.... the child can have family member at the pub eating nuts as a snack and pop in for whatever reason.
The only way to ensure this child is safe is that she’s fully aware of her allergies and how she manages them... there is no safe environment with a child with allergies even in their own home.
It’s been said on here multiple times and largely gets ignored 
UK Allergy is the UK leading allergy specialists disagrees with this policy.
The anaphylaxis campaign has NEVER promoted the banning of nuts, peanuts and other allergens... it’s creating a false sense of security for all involved and minimises that allergy self management and education is an absolute priority.