The nurses she could see on the nhs were unable to support her or to facilitate a diagnosis. It really really had more to do with competence than resources
What huge, contradictory statements. Only Dr's can diagnose. They often consult with nurses to get their opinion as to what is wrong, but the diagnosis rests with the Doctor. If there is no Doctor (a resource) there is no diagnosis. What has that to do with the Nurse's competence?
Also, no-one is saying that you weren't right to be angry about what happened. Most of us would be too. But the best way to get people to work with you is NOT to make claims which are demonstrably untrue and which will have no impact at all e.g. telling a nurse you would hold her responsible for your DDs death.
A complaint via PALS would actually have had some impact. The nurse would have been investigated and steps taken to identify what went wrong and how it happened, to prevent the same thing happening again. THAT'S how to appropriately respond to anger and actually get somewhere. If a formal complaint had gone in, the nurse would have shit herself and been much more careful in future.
Sadly, when people's understandable anger leads them to make comments which attempt to invoke fear and intimidation, MH nurses immediately emotionally shut off. We are trained to do that, or we couldn't deal with very unwell patients who may be angry for illogical reasons. If we didn't shut off, we wouldn't be able to avoid taking it personally, and that may then affect the quality of care we are able to deliver to that patient. But BECAUSE we have empathy, we know the patient can't help it, so we close down our emotions and just deal with stuff, so we can still care and help the patient without feeling angry with them.
Unless you have done the job, you have precisely ZERO idea of what we need to do to maintain our own mental health AND our ability to provide compassionate care. We aren't there to deal with ridiculous comments made by families. We would always help them make a formal complaint though. So take whichever tack you want, but your approach didn't exactly work did it?