Ann I totally understand where you are coming from. Surely if you are exhausted and out of it they will take the baby. Interestingly it was the one piece of advice my mother has given me - ask them to take the baby to nursery if I need to sleep. Anyway I asked three different friends who've had their babies at the private hospital where I'm having mine. One said they will take baby away on first night if you are tired, the other said it depends on the midwife, and the other one said the policy is that baby stays with you. I remember when my brothers were born and I'm talking in the late 70s early eighties here, and all the little babies were in rows in the hospital nursery. You'd go and look at them behind the glass window. So cute! Things have really moved on since those days!
Anyway at least my hospital encourages partners to stay with you.