As noted, late spring can be too early for Yellowstone. Sometime after Memorial Day things start to open up, depending on the snowfall the winter before. If you're looking at a June trip, Yellowstone should be on your short list. Amazing diversity of things to do. It's the first national park in the world for a reason.
If you're looking at April or May, I'd consider Zion, Bryce, south rim of the GC, and Mesa Verde. A variety of scenery and Mesa Verde is not only interesting, but educational as well.
Two weeks is just too short of time to see much of the SW, and I'm sure the kids would rather spend time somewhere but on the road. The trip out and back will be long enough.