Seriously? 15 minutes?
I don't see why you should have to say more if they have that much documentation in their hands. They should pay it because you pay your premiums. They should pay it because it isn't a cosmetic procedure. They should pay it because your daughter has so many other things to worry about, a hemangioma shouldn't be one of them.
Additionally, you should videotape it and send it to the White House. This is the future of health care ... begging for it in 15 minute increments.