With being licensed you probably need a contract signed anyway, might be a good way to broach the subject with the parent. Your coordinator will likely want to see that you have appropriate paperwork for all children in your care.

It is my policy too that no outside toys are allowed, and if they come then they go into the backpack immediately. I don't always wait for the parent to leave either, as soon as the child is undressed I get them to say good bye to their toy and have them put it in their backpack themselves.