If you're going to North Rim consider Zion or Bryce national parks for the rest of your time. Don't try to cram too much in that one week.
Zion, try to get a campsite on the river and the kids would have fun spashing... it's 'usually' a wadeable stream - not deep, unless there happen to be monsoon rains. Also, at the end of the shuttle bus drive in a 'trail' of sorts but it's a river trail and very popular to do in summer. Water shoes and a walking stick are advisable. Again, during monsoon storms it would be closed off because it would be dangerous but other times, just fine.
Bryce - temperatures would be cooler than Zion but no water play. Instead, hike down into the hoodoo formations. It's like a fairy wonderland down there. Go down 'Wall Street' trail and up another one... or up again on Wall Street to test your lungs!
