why should she trust them? they killed her kid.
Who is "they" and how -- exactly -- did "they" kill her kid?
Granted, the facts are there -- a live kid underwent surgery, a live kid came out of surgery and requested a Popsicle because her throat hurt (not uncommon after a tonsillectomy, if I recall grammar school mates' stories way back when), and then she began bleeding and went into cardiac arrest.
You don't seem to have your argument very well organized. You refer to a "comatose" (i.e. alive but in a coma) "dead kid" (i.e. NOT alive). In other posts you seem to be suggesting that the parents are correct and that the kid might wake up again, given enough time. Then you write that "they killed her" -- again implying that the kid is, indeed, dead.
If we accept that she is dead, then the question is what (not who) killed her. Certainly, nobody set out to kill her. The operation was more than a routine tonsillectomy, and I think we can assume that the parents were advised of that. But "the hospital" didn't perform the surgery. A surgeon performed the surgery. I don't recall seeing his (or her) name mentioned at any time, and I certainly don't recall seeing anything to suggest that the doctor was an employee of the hospital. Could have been, but also very well may not have been.
So ... did the surgeon botch something? Did the kid have some undetected problem that was triggered by the operation, or by the anesthesia? We don't know. Maybe the doctor goofed, maybe the doctor did everything right and the kid died anyway. It happens.
Unless and until we know who did what, and WHY the kid died, it is irresponsible in the extreme to make statements like "They killed her kid."