3. What are your average driving days? long driving days? look like mileage wise? Hour wise? I'd conservatively say I'd average 55-60 mph depending on the length of drive.
When you factor in stops (which you should take frequent breaks with kids that age) most on here average 50 mpg. Some will do more, some will do less, but 50 mph is a good number to figure on. Having traveled extensively with a young child (who is now 25) I'd head south to Myrtle Beach and/or the Outer Banks. Still warm but you've got beaches and tons of kids activities. Hiking with young kids in the kind of heat that you will experience in Utah will not be pleasant. The parks themselves will be pretty boring to kids that age. I would save those types of trips until they are a bit older and can appreciate what's around them. If you do decide to do your original trip I'd cut back on the places to visit and make sure you stay in campgrounds that have things for the kids to do.