My child didn't have sleep apnea, but had his tonsils removed, his adenoids reduced, and tubes put in his ears at the same time. I don't know if this is the same, but his tonsils were huge and I was so glad for them to be removed.
Ask for "giggle juice" (versaid) to be administered first so that she gets loopy and won't be scared. Ask the surgeon not to put the IV in her arm until she is asleep. (Perhaps the anesthesiologist will use gas.) IV's hurt and there is no good reason why she has to have it while she is awake, and you should stand your ground if the anesthesiologist tries to push you because of his or her convenience. (You can tell that happened to me.)
It doesn't bother me one bit or surprise me that they are doing this at a university hospital where they have a ped ICU. They are set up for children there. You don't really want to have the surgery where they are only set up for adults, right? The point is, they are making sure they can handle any surprises. Sleep apnea, if indeed she has it, is a serious thing and is hard on the heart. That's probably why they are being so careful. Just ask the doctor if you aren't sure about why they want a ped ICU at the ready.
I have read from other moms on here whose kids snored like freight trains, that once their tonsils were gone, their snoring ceased. I hope the same for your DD!