BUT it sure as hell isn't normal that her father is choosing her doctors

For this, I am curious about the girlfriend's perspective vs. the boyfriend's on on how much the dad is choosing and to what degree he is "wanting reports." And how often does she go to the doctor that this is a pattern that the bf has noticed in 2 years since many people go to their gp about once a year?

My dad is a doctor, and I will ask him for recommendations. Even a couple of weeks ago, I found a clinic I was interested in, and I sent some info on it to him and my main doctor in order to get their opinion on whether it would be worth pursuing or if I should go with another clinic since they are in a better position to know if the the treatments that clinic was recommending are "out there" or legit because I don't know as much as they do about medical research. I have multiple chronic health problems, and while I certainly don't give my parents a full report of everything that goes on at an appointment, it'a not uncommon for me to give them an update on anything new I have learned, any new recommendations given, etc. (They are in good health, but do the same for me, e.g. mentioning in passing that they had a routine cancer screening and it came out negative.) At one of my last appointments, my neurologist (who had been treating my rather rudely) prescribed me two new medicines, and I mentioned this to my parents during a conversation. My dad was quite shocked that I was prescribed those for multiple reasons, so I followed up with my main doctor and it was made clear that I was not supposed to take those medications and my neurologist had made a mistake.

TL;DR: If OP's girlfriend is not going into excruciating detail in her updates on appointments, e.g. just saying if she got a new medicine rather than describing how her pap smear felt, or if her dad has some medical expertise and he's helping her choose good doctors rather than arranging her medical life for her, I don't think this is weird.