In this situation I would be done! I would be terminating. I had a boy like this and I only lasted 3 days. I was already calling mom during nap time because the whole house couldn't sleep for the screaming. I had never had a child like that before and never had once since. I am amazed you are still going after 3 weeks of it. I was the 2nd daycare already with this little boy, the first one only lasted 1 day. The third one was a charm and he was fine in a few days.
You need to think about the children already in your care. If my child was being subjected to a child like that in daycare I would not be too happy. It is group care and you need to do what is best for the group and caring for this child any further is not good for the group IMO. Not all children are a good fit for every daycare, I think it is time to throw in the towel. I think you gave it an honest effort.
As for them sending their child after the child has not slept - why has the child not slept? illness maybe? A child at daycare should be able to participate in the routine of the daycare or should be kept at home.
Yes, I have in my policy that a child must be able to actively participate in our daily routine. If they cannot then they must stay home. I would include a child that has not slept in 32 hours as unable to participate.