We just took a 23 day trip from Maryland to South Dakota, Wyoming, eastern Utah and northern Arizona. To see all those areas involved a number of long days of driving. If you wanted to see the Southwest U.S. I would not go to Yellowstone. It is not really the Southwest to me. You can see a number of parks close together in southeastern Utah and northern Arizona. Arches and Canyonlands are basically "across the street" from each other. Just south into Arizona is Monument Valley and Antelope Canyon. If time permits it is less than a day from Page to the South Rim of the Grand Canyon. Probably less to the north rim although I have not been there. Antelope Canyon is a slot canyon that gives you unique photos.
Our entire trip blog is the attached link "Arches, Geysers and Canyons". Feel free to take a look