So the 1st aid was administered by pgl staff, not the teachers. Pgl chose not to send to hospital when the injury first presented and again when she saw them later. The teachers proved that they were more than capable of taking a child to hospital if needed as they did for another child. The teachers administered pain medication when asked for so we're aware of the injury.
It seems that several adults were involved with your daughter's care at several points during both day and night, none of them realised that the arm might be broken. I don't think their drinking had anything to do with the care your daughter received. Had anyone thought it might possibly be broken, they would have taken her to the hospital. They didn't take her, not because they had been drinking, but because they didn't think the injury warranted a hospital trip. I'm sure many parents have also done this, me included.
My daughter tripped at a holiday club, they called me to pick her up as her arm hurt, I didn't take her to a+e as it didn't seem that bad, it was only 24hrs later when she was still hesitating to move the arm I took her and we discovered she had broken her elbow. It's not always easy to tell, they treated her appropriately for the injury that they saw.
There could be many reasons they took a cab to hospital for the other child rather than driving themselves, the fact they took a cab does not prove that they were all drunk. Off the top of my head, a few reasons why taking a cab makes more sense.......Not all staff were qualified to drive the bus and they had to maintain male/female staff ratios on site so the only drivers couldn't go. They didn't know how long they would be at the hospital, and needed their minibus on site for the others. Parking a minibus at a hospital could well be a nightmare. Taking a taxi means they don't have to find their way around an unfamiliar town with the possibility of getting lost.