@Pepperedbeef there may be differences in types of schools but I work in a primary school kitchen which serves up to 440 kids, everyday.
We have separate areas and separate staff for veg prep, meat prep, sweet prep, sandwich prep.
We clean down between prepping cheese/tuna/ham sandwiches, and each type of sandwich is then wrapped and kept separate from the others. Each 'flavour' of sandwich also has its own set of serving tongs to eliminate cross contamination.
We have approx 28 kids with allergies, intolerances, religious, lifestyle choices and we prep for all of them. These include allergies to wheat, gluten, orange juice, eggs, legumes, milk, nuts, fish. We have pupils who can only have halal food, vegetarian pupils who can have fish, vegetarians who don't have fish, pupils who don't have pork/beef, we even have a vegetarian who can't have Quorn.
We cook gluten free foods away from gluten foods, and we endeavour to offer gluten free puddings whenever we can so that our pupils have the choice of a gf biscuit or a muffin rather than fruit every single day, we include them as much as we can.
We constantly wash our hands, change gloves, and monitor each other to ensure we do everything possibly to provide safe, non contaminated, good food for all our children, it's a basic requirement of our kitchen, it's actually nothing special! The op (or rather, her daughter) has every right to expect to be offered a choice of food that has not come into contact with things she won't eat, for any reason.