Your opinion is fairly bias, and perhaps a little study on the subject could help. There are many ways of dealing with them, but knowing how to do so, is the first step. Don't have breakable things in your house? I suspect those thousands upon thousands of families who have a member with autism, have more than plastic dishes and rubber furniture.
You said you have supervised a number of kids, but have you talked with anyone else who has? Probably someone with a bit more experience, a parent perhaps? It could help you out I am sure, but if neglecting the child is a reason for the behavior, the problem doesn't lie solely with autism.