Hi Wololo, Whistler is great - you can take a shuttle there from Vancouver (either downtown or the airport) see:
http://www.whistler.com/getting-here/road/shuttle/You don't need transportation while in Whistler depending on where you stay - the villages (upper and lower) are totally walkable and the town is really bikeable (you can rent bikes lots of places) and there's also some transit.
Activities at that time of year are hiking, walking, golfing, biking (including downhill) and you can also go up the mtn and sightsee and do the peak to peak chair. There's also a great playground in the Olympic Village (you can't miss it, very easy to find) that your kids will love.
Not sure how long you are thinking of staying there but you can do Whistler in a day or 10. You can see lots in a day for sure if that helps with your planning.
Now you don't need a car if you are going to stay in Vancouver either. Transit and Skytrain are amazing. In fact I travel there frequently (grew up there) and if you are downtown I won't do anything but Skytrain. See:
http://www.translink.ca/en/Schedules-and-Maps/SkyTrain.aspxHave fun!