M.M.
Hi D.!
It sounds like you are the same situation A LOT of us are in. We take our kids (4 and 5 yrs old)camping over the summer. If you are not into the "tent" thing you can always rena a cabin or yert in Golden Gate State Park (Reverands Ridge). Its only 1 hr from Denver up Coal Creek Canyon out of Golden. Its right at the Peak To Peak highway. Totally away from town and still close and cheap. reserveamerica.com will give you all you need to know. Just put in Golden Gate State Park for the Park name to make reservations. The cabins are only $60 bucks a night in the winter. They are heated. You can build campfires, grill and have a blast. We hike and snowshoe there in the winter. In the summer you can drive up the road to Peaceful Valley and ride horses or stop by Camp Dick and hike and play in the creek. Bring your bikes too. The kids LOVE being in the mountains! Another idea is to get a room near Lake Dillon. You can bike the trails (use a tandem attachment for the 3 yr old), nature trail hikes or rent a boat. Get a hotel with a pool!
Check out some day trips too like the Ceran Saint Vrain trail out of Jamestown (west of Boulder) there is a wonderful, beautiful easy trail there for the kids and a creek to wade in and throw rocks (to the right of the foot bridge). Also Eldorado Canyon has some great stuff for kids http://www.localhikes.com/Hikes/measa_trailhead_2082.asp playing in the creek is HUGE fun here...
good luck!