You're going to be pressed for time if you leave Charlottesville, want to detour west to Cades Cove, and then make it to Asheville the same night.
I-64 to I-81 to I-40, exit at TN 66 and go south to Sevierville, then US 441 into the park (using the Gatlinburg bypass if you don't want to get caught in the traffic there), to the access to Cades Cove.
On return, US 321 north out of Gatlinburg (East Parkway, the turn is, IIRC, at Traffic Light #3) to I-40 to Asheville.
From Asheville, I'd highly recommend US 23 into Georgia, then the interstates on in to Atlanta. Easy, scenic drive, which should all be four lanes now (when I drove it years ago, there were still a few two-lane segments of 23 in Georgia that were under construction).