Some hotels have pools that are open year-round, though you should always check as this is the time of year they'd close them for a couple weeks of maintenance etc.
Bellagio
Hilton Elara
Excalibur
Gold Coast
Green Valley Ranch
Palazzo
Paris
Platinum
Sam's Town
Vdara
Wynn Resorts

LV also has a terrific Children's Museum that's worth a couple of hours, and if the 2 year old is interested in dinosaurs, a nice Natural History Museum. Also check for holiday events at the Springs Preserve....and one caution, when New Year's falls on a weekend Vegas is crazy-crowded and rates are sky-high. Since Grand Canyon and Hoover Dam are the main things on your radar, you might want to check for rooms in Henderson or elsewhere.

(Oops...Just re-read and noted that Vegas is the first part of your trip and hotel already arranged....great!)

Day 3 - grand canyon - (GC night stay)
Day 4 - grand canyon, hoover dam - (GC night stay)


You're going to want to visit Hoover Dam on day 3 on your way to the Grand Canyon, not on day 4. Make sure you give yourself enough time to see Hoover Dam and make the long drive during daylight so you get to the Grand Canyon before sunset.