the right to speak with each child alone
What RIGHT does government have, to speak with any child alone?
If the government isn't allowed to speak privately with the child, how will they be able to badger the child into testifying that their parents are abusing them? Any child can be induced to say anything you want if you keep after them long enough. This was demonstrated when Janet Reno was Florida's state attorney and several innocent people were convicted of child abuse on children's testimony alone. Unrestricted and unmonitored interviews would be very helpful to the government in taking home schooled children away from their parents.
You will notice that I gave the government the benefit of the doubt by not mentioning that speaking alone to the child would also be opportunities for abuse, as well.