Auntevil, both my ds and I see rheumatologists regularly throughout the year, they manage our eds. Ds also has a paed and two orthopaedic surgeons, paed cardiac surgeon as well as physio and orthotics and clinical psychologist, all connected to his eds.
Midnight - it very much depends on the pct it would seem, but there is no reason to assume your dd will be discahrged by the rheumie.
Bizzey - my ds has very big blue eyes, with blue tinged whites, as I used to have but now are blood shot! The Optician says his eyes are fine, but he has an almost neglible amount of pigmentation at the back of his eye, which is why he is so affected by bright conditions, and needs sunglasses. Blur tinged whites is a symptom of eds.
My ds has a very large foreskin and got recurrent balanitis (sp?) infections. Had to teach him to wipe the end of his penis dry after every wee, this cured the problem that 3 gps creams and AB had not been able to cure. Not related to eds, just happens sometimes, as does tight foreskin...just keep and eye on it....iykwim 
Plus - laughed alot over a long time re "What do rheumatologists do...! " thought has crossed my mind many times.
Seriously - they are the joint and connective tissue specialists, so they monitor joints, recommend physio programmes, send out to other specialist teams to get other affected areas checked out eg. heart, neuro for migraines, orthotics, gastro etc. But they are supposed to manage the whole child. They will take progressive xrays...to montior joint deterioration and do blood tests to keep eye out for rheumatoid arthritis too, as well as generally inflamation markers in the blood and urine.
Hi Ariane -sorry about the bursting veins it is horried I am sure. I didn't have that but dreadful varicose veins, which still plague me now.