OP, I really hope your DD has been seen now. It's crap to have to wait so long. FWIW, at the ED in my hospital, the paramedics will run patients straight through to resus (the ones that need to be seen right away), so you wouldn't see the major cases being checked in by paramedics at reception. Doctors may be pulled from A+E to other wards, or the A+E patients maybe waiting for specialty teams (surgeons, ITU, anaesthetists, gastro, paeds, urology, gastro, resp etc) who may be attending patients in other parts of the hospital. If resus or majors is full, then the staff could very well be in there attending to patients. They can't leave those critically ill people until they're stabilised and it is safe to do so. My ward patients are level 2 and when they deteriorate, you have to work quickly and stay with them until they're stabilised.
I work on a (very busy and acute) ward, as a senior nurse. If you see me sat at a desk or on a computer, it would be because all our notes, drug charts etc are on computers. Legally, I have to document everything I've done with a patient: so all referrals, notes, plans, updating handovers/charts etc etc. I have to sign the drugs I've given, on a computer. I also have to use the computer to arrange porters, order items/drugs/ward supplies and deal with staffing. So it might look like I'm doing nothing (and I bet that would be really annoying to people!) but believe me, I'm working. I imagine that it would be the same with the staff at your A+E.
I can't speak for other hospitals, but I know that where I work there is a massive push for speedy patient flow and making sure beds are freed up promptly to allow people to get through the system quicker (I understand that hospitals can get fined if there are delays or breaches). Bed moves and transfers will happen at all hours of days or night (there used to be fewer moves at night time or during meal times - so patients can sleep/eat - but that's gone out the window now). We often have patients boarding in corridors on our ward (not nice for the poor patients at all - we care for them as best we can). We battle to make sure we get patients to our ward so that they can have prompt treatment, but also to make sure that patients don't get discharged too soon. On the other hand, there are delays for patients needing care packages and placements as there is not enough in community, so often they will have to stay in hospital.
All of the above won't help you guys, and I'm sorry for it, but I do hope that it does give you a bit of a picture of what goes on behind the scenes. I wish you guys all the very best and that your daughter has a speedy recovery xx
PS I work in an NHS hospital, and yes, we're also short staffed for the acuity/dependency of patients that we have on our ward.