I once did discharge myself and my baby. It was DD3, so I had already had two previous babies.
She had been born slightly prematurely, at 35 weeks but was feeding well (on their prescription formula), pooing and weeing well and had no other problems at all. Not even any sign of jaundice. She was a very reasonable weight too for the stage of pregnancy she had been born at ( 6lb 8oz). I had had a caesarean, but was doing fine too and they were ready to discharge me.
All doctors agreed that there was nothing wrong with DD and most said that they’re would discharge her, but there were a couple who, for reasons known only to themselves, said simply that preterm babies should remain until 6 weeks past their due date. Paperwork for discharge or anything else seemed totally elusive. So I was stuck. I wasn’t convinced on the need to stay and nor were many of the other staff. So I decided it was bollocks and told them that once my DH got there later that afternoon we would be leaving. With our baby.
Funnily enough, that broke the deadlock. The paperwork magically turned up and was signed. As did the bounty pack and all the other bollocks that they discharged you with back in those days (2002, that “baby” will be going to uni in October). Social Services were not involved or even mentioned. We simply went home.
Ask for a meeting this afternoon if possible. Certainly insist (calmly) on having a clear explanation of the reason, medical or other, why you must stay in. Test results can always be sent directly to your GP if not totally urgent, and you can be advised from there.
If they come up with nothing then say that you will be leaving with your baby at XXX time, thank them for your care etc.
This all assumes that there is nothing else going on that you haven’t mentioned of course, but I actually don’t think it is uncommon for this sort of thing to happen. It can be down to disagreements between staff and/or administrative cock ups.