No, you could also ask for a cup of ice water, some will give larger ones if you ask, if they won't, figure out how many of the kids cups it will take to fill it and just ask for that many cups.
It's sad that they won't simply fill it for you, seems like such a waste of cups to me. Also, if you go anywhere that has self serve machines, just fill it with ice and/or water, you might get some strange looks, but what are they going to do?
By the way, here is a list of places that have self serve machines:
- Tangaroa Terrace
- White Water Snacks
- Rancho Del Zocalo
- Plaza Inn
- Red Rockets Pizza Port
- Boardwalk Pizza and Pasta (Note: This location does not allow refills, unlike all other locations that have self serve drinks, but water should be fine as it is free anyway)