A simple xray will show whether she is truly constipated or not. You can see the impacted bowels. I don't know, but maybe they could even tell with a sonogram. I understand that people, especially children, should not be exposed to MRI's and xrays unnecessarily, but this seems ridiculous that the doctor wont prescribe sedation. I would insist on an xray or ultrasound to prove the constipation, and if they agree and it is that, you will know what to do from there. If the doctor refuses or the results don't show constipation, get another doctor. You don't have to stay with the same pediatrician.
Did the doctor prescribe anything for the constipation? If you are constipated to the point of pain (and yes, it can get pretty bad), something needs to be done medically. Fiber and prunes won't cut it. There is a liquid laxative you can drink, makes you feel awful and crampy, but it takes care of it. I don't know what they give to children, but that is what they do for adults. If the doctor hasn't done anything for her at all, I would not hesitate to find a new doctor.