Most importantly, you need to find a pediatrician you're comfortable with. Being informed is so important but you also need to recognize that the pediatrician is who she is because of extensive medical training - training that non-medical-professionals do not have. That doesn't mean they aren't ever wrong. It just means that sometimes they know better than we do. I would NEVER blindly trust my pediatrician, but if I need to make a medical decision, I definitely seek him out for counsel and sound advice.
It sounds like you are very smart and probably did your research on this pediatrician before you selected her. If this is the first time you've disagreed, I'd say give her another 6 months or so (you'll have a lot of appt's in that time) and see how it goes. This might be the only issue on which you two disagree.
Bottom line: I think you need to figure out if this is a big enough issue to go through switching pediatricians. No one can judge that except you - you know what/how much you can let slide and what's a sticking point. I think you should give her another chance over the next 6 months but be guarded and observant. In the mean time, you can be looking in case you need to switch, but you'll still have her to attend to your childs' medical needs should an emergency arise.
I do feel that, sometimes, doctors forget the families and emotions behind the
patients. Sometimes I feel like the doctors (not just pediatricians) look at us like a chart of issues and not a person who needs help, and they forget to listen to us and have compassion - they are just interested in solving the medical problem and moving on. If you find a doctor who can listen and be compassionate, I think they would likely be open to any parenting style/choice (anything that's safe, that is!).
My only rec: have you considered a D.O.? Their medical philosophy is just a little bit different than an M.D. and they have all the same training and credentials.
I can't recommend my pediatrician... I like him a lot but he kinda pushes pharmacology too much for my taste. I'm more of a less-is-more kind of gal. But his office staff is awesome and I never wait in the waiting room more than 10 minutes. I LOVE that part! :-) GOOD LUCK!