My daughter has seen multiple psychologists, psychiatrists, therapists, in addition to medical specialists (just so you know that we have been through the behavioral stuff on many levels).
First off, I'd like to suggest that perhaps you are focusing too much on speaking to a primary care physician for your daughter's issues. It doesn't sound as though your daughter has medical diagnoses that would impact her behavior. Your PCP is the person to speak to regarding immunizations, infections, diseases, well-child exams, etc.
I would immediately schedule a psychiatric appointment (with a psychiatrist, who is also a medical doctor and who can prescribe meds if absolutely necessary, rather than a psychologist, who would be good to see after diagnoses were made by the psychiatrist). If you can't find one by looking at www.healthgrades.com, or searching doctors on your local hospital's website, then call your insurance company and ask them for some names. You want a psychiatrist who sees young children specifically.
As for talking to the doctor with your child present, that's not always a bad thing if done properly and with the doctor's guidance. The parent shouldn't express outright frustration (like "she's driving me crazy and I can't take another minute of her attitude"). The parent can address both the doctor and the child, and can be honest ("I admit I'm at a loss about how to help [daughter] when she gets so angry" or "it seems like [daughter] is having problems at school and I'd like to hear your suggestions about how to deal with them"). Take the child into the conversation, using her name, and inviting her to weigh in. It can be really helpful to have a professional to whom to be accountable when dealing with a behavior. The doctor can lay out a plan which includes the parents and the child ("when [child] starts having a temper tantrum, parents are to stay calm, and lead the child to her room" or "parents will schedule meeting with the teacher and ask these specific questions, then report back to me").
Having both the parent and child at a psychiatrist's appointment can give the doctor valuable insight as to how the parent is acting, and how the child is acting. It's important to make sure your attitude is a willing and receptive one, and that you're going to be able to take advice well. It won't work if you storm out of the appointment grumbling "that shrink thinks I don't know how to be a mother to my own kid" or "how dare that doctor tell me I'm not listening to my kid". There will be, almost inevitably, some specific suggestions about how to parent a challenging child. My husband and I both have college degrees, but we had to sit at a little table with our doctor and our daughter and both learn how to handle her severe aversion to food (due to a medical issue) when she was 2 1/2 years old. We already had a son but we had to be willing to be told that what we were trying (which was EVERYTHING) wasn't ever going to work. So your attitude is important.