How fast is the heart rate at night?
Have they tested her thyroid?
Abnormal thyroid can cause the symptoms you are talking about that is why I asked about it. They are usually done with routine blood tests.
CHildren do have fast heart rates, I would expect hers to be in the 90-110 on the outside of normal. But they are usually regular. However, with respirations and deep sleep they can be a little irregular normally.
Heart problems usually do not cause sleep apnea but sleep apnea can cause heart problems if not treated long term.
With you daughter being so young, a cardiac evaluation is important and it seems like that will be done soon. Sometimes it is hard to find a pediatric cardiologist!
I wish I could give you answers as to what is wrong but certainly all of the tests have to be run first... is there a way (to ease your worry) to see if they can put her on a waiting list and do any of the tests sooner? You could call and ask them...