Yes, expecting to be able to eat a sandwich when you work from 9-3 is perfectly reasonable.
The first thing I would do is check your local labour laws, because many areas have regulations about breaks, even for part time or shift work.
Then, I would talk to your employers, but be very careful about how I approached it. Maybe something like "I wanted to clarify the lunch/snack break arrangements with you, as I've noticed that a lot of the kids are uncomfortable stopping to eat, and productivity drops later in the day, as people get hungry and grouchy and can't concentrate as well.
That way you aren't asking for permission for a perfectly reasonable request for basic functioning; you're asking how best to schedule it. That way your boss can't slide around it - they have to say right out "My employees are not permitted to eat lunch", after which you can act surprised at their demands.
If they do ban lunch, and have the right to keep their employees from eating, then personally, I'd be tempted to arrange with my coworkers to cover each other while we ate our sandwiches.