You've had a big shock. It's horrendous getting those phone calls from school when you don't know how bad things are going to be. Your child is in pain, the world momentarily stops turning and even when you know things are going to be okay again you need to unwind the pent up emotion.
Your title has been read by many as undertones of anger. Anger that you say you're not feeling but your emotions will no doubt be in turmoil (even if you're doing the graceful swan thing on the surface, your mind is no doubt racing).
I've had a couple of A&E visits with my DC. One because DS1 fell down the school stairs and was concussed. He was meant to be in a science lesson, he's autistic and has support in school. There had been an incident and the teacher had been delayed so DS took himself from the lesson to the quiet learning area as he doesn't cope with change and in his frustrated state miscalculated his step. He has pain threshold issues and wasn't sure if he'd been knocked out. The steps are concrete so he was covered in bruises and had an egg on his head.
We did the sitting in A&E thing - they were fab (our NHS is such a wonderful thing, I'm grateful everyday for its existence). The consultant suggested a large brandy as appropriate treatment - I was a bit shocked (again). The brandy was meant for me.
DS's wonderful teachers had left messages when we got back from our long A&E trip and it was after school hours so I couldn't contact them. We have a good relationship because being Autistic DS has an adjusted curriculum and high support needs so we have regular contact.
I emailed all was well but DS would need to be off for a day or two due to the bruising and concussion.
I thought they knew me quite well but when we actually spoke the next day the relief in his teachers voice, I won't forget. She cared as a person and parent herself first, but also because that horrendous constant undertone of litigation, investigations and life being on hold.
Teachers and coaches who are in it for the money are few and far between. Lunchtime coaching is pretty rare in my schooling experience too.
I think the way you've proposed moving forwards sounds appropriate and positive.
Hope that you and your DS are able to get some rest today. 