I think you've misunderstood what is available at Coral Reef. It isn't that you can order a Pina Colado and say make it w/o rum, but rather CR has a couple of specialty drinks with are non alcoholic. My mother had the Strawberry Stinger, probably like a daiquiri, but I can assure it she ordered the stinger, daiquiri was never part of the discussion. Now what surprised us is that she refilled the stinger, not sure that's usual, but she did it on her own, we did not request the refill. I had a soft drink as did our 5yo.
OP - coffee, tea, milk, soft drinks and in some cases milkshakes, smoothies and select specialty drinks apply on the DP. Best thing to do is to ask your server what options you have.