I'm pretty new to the diagnosis of my autoimmune so I won't be of much diagnostic help. I saw your post didn't have a response yet, and I had hoped someone with more of a knowledge base would come offer you some suggestions to look into.

Until you get some direction or answers I just wanted to say you are not alone in your worries and frustrations. I was undiagnosed for 7 years, as auto-immune is notoriously difficult to diagnose. I know that's not really helping... I'm sorry. I can tell you when my hands stopped working, it scared me something aweful. I bipassed my primary care as I don't require a referral with my insurance and scheduled with a neurologist. It was 3 weeks before I could even get the initial consultation, and then another month before she scheduled further testing. Then, I was referred out to a Rhumatologist, and the one at the university where my neurologist is was going to take 9 months for an appointment. Unacceptable! I called around and found a rhumatologist that got me in within a week.
So, if the docs are making you wait, call around. Get recommendations from others you personally know if possible. If you don't have to have a referral via insurance, and it is suspected autoimmune please find a rhuematologist asap. Scheduling an initial appointment before the testing comes back may save you some of the waiting time. If they figure it out in the meantime and you don't need a Rhuematologist, you can always call back and cancel. (I know you mentioned specialists, but not which ones.)
I hope your daughter gets the right information and help soon, and a relief from worrying for you! At least if you know what you'ree fighting, you can have a plan. When there is no diagnosis, there is no set treatment plan and that is frustrating.
Oh, and the only other advice I can offer, that helped get me diagnosed. Get copies of all her doctor visits, and bloodwork, scans, ect and keep them with you and take them into ever doc & specialist appointment. An old bloodwork panel helped show the neurologist a particular test had increased exponentially within the last 2 years, that she didn't think much of without comparing the old and the new. I now ask for copies of everything before I leave the office to make sure I put it in my folder. Also, have her start recording everything in a journal/diary/smart phone app. What her symptoms are, how frequently symptoms occur, time of day, activity that brought on symptom, anything that relieves symptom, ect... Even if they're the same every day. You may find a pattern of time of day, for example, my hands hurt more when it rains, so I have more issues then.

Again, good luck to both of you!