Lauren wrote:
"Southwest" is huge - suggest you narrow your area and allow time to fully enjoy the places you choose and not spent your time visiting them thru a window.
Choose your destinations based on your family interests and enjoy them.
I would agree. The suggestion to hit Yellowstone and Grand Tetons only is your best bet. There is simply no possible way to "see it all in only 2 weeks, and attempting it will kill you.
There's plenty to see and do in Yellowstone and Grand Tetons to take up the entire 2 weeks, never mind your time getting there and back.
When you have 3 to 4 weeks, you might consider doing a circle around the Grand Canyon. It'll take you 2 of those weeks just to circle the canyon, and do side trips to Bryce and Zion, which, although canyons as well, are as different as night and day. The North Rim of the GC is very different from the South Rim as well.
The entire southwest is so huge, and so varied, with so much to see and do, you would need more like 3 or 4 YEARS to get to everything.