Our nursery only offers cows milk and rice milk. My girl can have rice milk. Dunno what they would do if a kid had a dairy and rice allergy.
Idk about daycare, but in elementary school if ur kid can't have dairy you have to provide them with their own milk
Ours offer soya or oat as alternatives but I send soya growing up as it has more nutrients If he can only have coconut but they have other DF options I think it makes sense they ask you to supply