Oh boy, have I been here! I am a home daycare provider and I have had two children in my care that did this-the key word being HAD! It was very difficult for myself and the other children in my care. I eventually decided that if the parents were not going to admit that there was a problem, then I would have to quit the child. I felt that by doing this that there was a better chance that the child's problem would be noticed. If you quit and the next sitter says the same thing and the next and the next, then eventually the parents will have to look into why their son is doing this. Chances are the nanny was not fired, I am almost positive she probably quit.
Both of the children I watched were the only children in their household. Both sets of parents were very soft spoken and kind. I felt that it was sensory overload for these children to be in a home with four or five other children. They just couldn't handle it. I definitely would start advertising your daycare and see if you can get more children. Once you do that, then I would suggest telling the family that your home is not suitable for this child and that he needs more one on one attention-the nanny is probably the best choice for now, but he does need to be with other children, but that is really for the parents to decide.
It is such a hard situation and I know that you are doing your best-remember that. If you didn't care so much about him, then you wouldn't be trying to help him. Just try to not get too frustrated and let anger get the best of you:) In one situation, the anger and frustration welled up so much that I said some things to the parent that I regret. Just don't let it get to that point.
One more thing, you know when it is affecting your family when your daughter says, "Make her stop crying mommy, please make her stop!" Best wishes to you.