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Yes, it's feasible to get to the Grand Canyon on a one week RoadTrip from Denver, but it would turn that trip into one that is mostly about driving rather than one that is mostly about seeing a few places in some depth and having some quality time with your Aunt. A more reasonable itinerary would go something like: Colorado Springs and environs, Great Sand Dunes National Park, Mesa Verde National Park, Canyonlands of the Ancients National Monument, Arches National Park, Colorado National Monument and back to Denver. Run that by your aunt and see what she thinks of it. If she's up for a little more driving, then you can consider adding Monument Valley and the Grand Canyon.

AZBuck