I'd seek a second opinion and keep pushing for an answer. Get the blood results for iron (including serum ferritin for her iron stores and vitamin D to see how far they are into the normal range as you can be in the normal (but not optimal) range and still have symptoms. If she eats a varied diet, is it possible she is having trouble absorbing nutrients? Something like undiagnosed celiac as they can have issues with vitamin D.
You mentioned your daughter was previously assessed as hypermobile, how hypermobile was she? Sometimes people with Hypermobility Syndrome are no longer hypermobile (the muscles have seized up around the joints), but still have HMS. I have read that hypermobility + pain = HMS, not sure if that is the case.
I'm hypermobile in many joints, had what seemed like fibromyalgia/HMS. To illustrate how sometimes doctors do miss things, I saw a consultant privately who was the authority in the UK on hypermobility for severe chronic arm and back pain and he didn't pick up the hypermobility! Just discharged me saying I didn't have arthritis and there was nothing he could do. To be fair, at the time I didn't know I was hypermobile and thought everyone could put their hands flat on the floor and bend their elbows when they did a forward bend from standing, it was my normal.
Years on, I'm a better place but it has been a lot of trial and error. I've never had a diagnosis, my physio put me on to a remedial massage therapist who helped so much. More torture chamber than spa treatment, very much like old school physiotherapy where they manipulated the muscles rather giving exercises but it worked for me. It was the very tight muscles causing the pain, they were all bunched up with lots of little granules and when it was at its worst caused nerve pain. I felt like my arms were on fire along the nerves. The remedial massage therapist was registered with LCSP www.lcsp.uk.com/, they have a list of therapists. I'm not sure if they work with children but I'm putting this out there for any adults with similar issues.
For the fibro, over the years I've used yoga (the gentle kind), find meditation helps with anything muscular to help unwind, body scans (where you imagine every muscle relaxing in turn) seem to help a lot at the moment and am not getting so much muscle tightness and have managed to reduce the physio/massage routines down completely.