I would also not allow children in my cupboards or frig- ever. My kitchen is gated off.
But, you might offer a new service- for $25 a week you will send home a healthy to go snack for the car. mini bottle of water a baggie of something, goldfish, cut up apple, cucumber slices. You get the idea.
If they do not opt in to the new program, you expect the parents to enforce no food from your house. If their child "helps themselves to a snack" it is $25 per time inconvenience fee.
I would work it something like- I am now offering a new program! I will be offering a healthy take home snack each day. It seems that some children are very hungry at pick up and this will give them the opportunity to have a snack in the car on the way home. I will provide a water and a baggie with a snack to go! The price for this service will be $25 a week. If you opt not to participate and your child insists on a to go snack, it will be $25 per incident since I will not be prepared to provide a snack for your child. I am so excited to be able to provide this service for you!