I have raised two rather good kids. One boy now 27 and a girl of 21 now.
Boy was pretty much without major injuries, but the girl was a different story. I have once actually proclaimed that: "She will find a way how to kill herself with just about anything. For example, she broke her finger with her backpack going off a school bus. And yes, I was accused of abusing her at the hospital. I can tell you that I really felt like throwing a lot of abuse at them, but things do not work that way in such situations.
From what you have described, I would leave the things go their own way for a while. As a defense against your specialist doctors, I would grab the document you found regards the child growing and bone break healing x-ray expression and rub their noses in it. Politely, but persistently. They sure will not like it and will have all kinds of comments on an amateur teaching the birds fly. You can then as well tell them that you will seek a second opinion and leave it at that. As a safe guard, you might want to have her checked in lets say a month again, but other than that, I would stay away from them.