Welcome aboard the RoadTrip America Forums!
Yes, you can 'easily' do everything on your list, and then some, as long as you have enough time (and money) for the trek. I did a quick map that just connected all the spots and areas in your list and continuing on to New York City, and came up with a total mileage in the neighborhood of 4200 miles. That would require about eight days of driving. Add in time to see the sights you'll be driving to, take some hikes, and visit with your partner's brother and you're looking at about three weeks as the minimum I would want to have available for this trip. But with that (and maybe a little more time) you can not only see everything on your list, but also such places that would be near your general route as Yosemite National Park, Death Valley, Monument Valley, Mesa Verde, the Black Canyon of the Gunnison, Capulin Mountain, Cadillac Ranch, the Natchez Trace Parkway, Memphis, Mammoth Cave, the Blue Ridge Parkway and Appalachian Trail, Washington DC, and others. On second though, maybe you'll need at least a month.
At this point, you should get yourselves a good road atlas of the United States and start plotting out a basic route and seeing what's along it besides your own 'must' sees. Once you've got a basic idea of where you want to go, we can help you make the best of it by directing you to some of the lesser known sites and sights that you might otherwise miss.
AZBuck