In my opinion you will have plenty of time with three months and you are leaving at a good time. We have made two loops from NJ to the southwest and then up to Yellowstone and Grand Teton before heading for home. We never seem to be able to get away until the second week of May and the heat in NM and AZ is too much for our comfort by the time we get there a week or so later. We like to get to Yellowstone and Grand Teton by the beginning of June to beat the crowds that show up after school gets out. We have been snowed on up there a couple of times in early June, but it melts quickly and doesn't delay driving around.
You might want to add Carlsbad Caverns in southern MN. It's a bit out of the way, but well worth the extra miles. In AZ along I40 are Petrified Forest and Meteor Crater and along route 89 north of Flagstaff, Sunset Crater volcano plus Wupatki National Monument on the way to the South Rim.
Agree with the suggestion to spend time at the Parks in UT. Bryce Canyon, Arches and Canyonlands are our favorites (so far). UT route 12 between Bryce and Torrey is one of the most spectacular drives in the west.