In reply to el diablo:
Another regular stayer in Camping Dolomiti in Cortina area - a nice site, but have never seen water in the pool unless it rained! That said we're normally there in Sept, so out of peak season.
Depends on what you're looking for to do with the kids and their ages, but I thought Canazei area was better looking than Cortina for families.
Camping Marmolada in Canazei it's self is grim - avoid! Camping Miravalle further down the glen was much better. A good sized common room, drying room and stuff like table football for kids on wet days. Pizzaria / bar on site too. No pool though!
Decent first via Ferrata on col rodella, easy access cragging on the sella pass and a climbing wall / kids amusement park nearby if weather poor high up. You could cycle up and down the valley on off road tracks as well I think (winter x country skiing trails) to visit other villages. If you are happy to drive an hr, loads more child friendly cragging.
Canazei and the village the campsite is in (forget it's name) are smaller and less in them than Cortina though.
I've a wee girl just coming up for 1 so have been thinking about places we could go on family holidays in the mountains a fair bit lately!
Not to say there isn't plenty for kids in Cortina, but wasn't as obvious when I was last there 2 years ago.