That is a pretty harrowing story and no mistake. But folks have to be rational about this and using a near death to your baby scenario to illustrate health economics is hardly a stable place for a level headed discussion is it!
When I was still in software, the project management company I ran had quite a strong base in pharmaceuticals. Clients included GSK and notably Pfizer. The latter spent circa $50 Million on a combination of our software and consulting to implement it and the reason was they wanted to reduce their time and cost to market of any given block buster drug. Because of FDA and our equivalent safety regulations, the cost to get a significant new drug through clinical trials with all the R&D can be up to $500M. Combine that with the time limit on patent laws and you start to develop an understanding why the drug firms want to claw back their R&D investment. Of course they make substantial profits but look at the increase in health outcomes we've all enjoyed over the last 50 years. Staggering improvements in all areas including the big ones like cancer and heart disease. The fact is that whether peoples personal politics agree or disagree with it, a market economy coupled with our superb NHS is a business model that has improved clinical outcomes at a staggering rate. So much so that now we cant afford as a country to pay for their extra longevity. The model is so successful its driven the pension crisis.
It's also true that "some" procedures are better done in the private sector. Simple, repeatable, non chronic procedures can easily be handled by the private sector more efficiently than the NHS. Where the NHS scores really highly is in complex, chronic, multi-faceted diseases. Exactly like the kind my family has been through recently. Cancer being one and a rare bone disease requiring a specialist orthopaedic hospital the other. Take my sons case, his bone disease is so rare there are only about 300 cases in the country. He needed a specialist, research, teaching hospital where the decision making is at the cutting edge of knowledge on orthopaedics. Not high street cataract day surgery which can happily exist in the private sector.
I think that based on need, there is room for both but we do have a staggeringly valuable resource in the NHS and we should never lose sight of that being our primary health care provider. If more funding is needed, I for one would happily accept a higher personal taxation burden on NI.