My father was a hospital director before he retired, my wife is a doctor, and I used to work for a hospital "working" with insurance companies, so I think it's at least fairly safe to say I have some personal experience with this system outside of being a patient. Saying "doctors suck" is like saying "mechanics suck" or "lawyers suck" or whatever. Medicine, like any other profession has it's share of the good, the bad, and the ugly. Also, like others have already said, there are a sh*tload of problems with our health care system that have nothing to do with doctors, and some problems that do. Now add a society wehere everybody wants to sue somebody and the f*cking lawyers (yes, I'm a lawyer) into the mix, and you've got one big stinky mess.
By the way, my guess would be that the reason they didn't just do a blood test to check for appendicitis is because you said she had been having pain for years and/or months. Pretty sure that the vast majority of people with appendicitis suffer from a ruptured appendix within a matter of a few days from the onset of sympoms. Chronic appendicitis, which is what you are describing, is a pretty rare diagnosis.
Either way, I hope they get it figured out.