I guess I'll always be unable to understand other people.
The parents' predicament is one I wouldn't wish on anyone and in some ways one that I've already been through.
When the neurologist said he wouldn't preform an EEG on my brother until the next doctor came in 12 hours later, I told him I'd walk in there, figure out how to do it and do it myself. I gave him until the time I was back from smoking a cigarette to make his decision.
The rest of the story is a little gory and technical, but suffice it to say that each time a barrier was put up, I just went through it, without hesitation and without lawyers, judges or cops needed.
Same here.
A tracheotomy is a fairly simple and common procedure and can be and has been done many times by laypeople with minimal instruction. The tools needed are a sharp knife and an adequate tube. Two finger's width above the "V" at the top of the breastplate is the location, cut through the fibrous tissue about half an inch down and insert tube.
Disinfect and dress wound. That's it.
Explain to the doctor that if he won't do it, you will.
Case closed.
