I fully understand why Ms Dance would prefer to move Archie out of the hospital. When my mother was in hospital long term, I had this increasing sense of dread every time I walked in - the staff were great, it just felt a very stressful and depressing environment. I would assume, too, that it is indeed noisy in PICU; even with the door closed, there will be the noise of other children's machines beeping, alarms going off, staff and visitors asking etc.
But the major hurdle is actually achieving the move, which looks near-impossible, and the family must be expecting the hospital to jump all sorts of hurdles to make it happen - because, realistically, there is zero chance of finding an appropriately equipped private ambulance staffed by private medical staff with the right level of training and expertise.
The ideal would be to find some sort of compromise, and I strongly suspect that is what the hospital is trying to do - e.g. a bed in a quieter single room within the hospital, if such a thing exists. The court will also be leaning on all concerned for that purpose. I really hope they achieve it.