If the parents are already providing meals, it is really simple to have them also provide personal utensils and serving dishes as well. All you would need to do is maybe rinse them and toss them back into each childs bag after meals for washing at home. Each day they should come in with fresh, clean, personal use items.
If you don't want to rinse them, you could even have them toss in a "dirty bag" ziplock that the dirtied dishes go in for rinsing and washing at home. That is how it is done throughout their whole public school experience.
Unless I am misunderstanding your post.