I-26 is a fine road, not many pot holes, good interstate. Just north of Spartanburg, SC, you will encounter the Green River Gorge. It is a 7% grade and goes for about 5 miles. Take your time and it will be fine. Just north of Asheville, NC is Sam's Gap. It is also steep and has a few curves on the way down into Tennessee. The speed limit is 45 through this area. Again, just take your time and don't try to push it.
We travel these roads all the time and don't have problems, but we are also used to travelling the mountains. You can do it, but don't try to be in too much of a hurry, stay in the right hand lane and don't sweat it.
Once you get to TN, it is straight sailing along the way into Virginia. The interstate ends, and becomes Rt 23 North. This is also a 4 lane highway with some curves and a few hills (which you would probably say mountains). About 25 miles into VA, you will need to turn onto Rt 421, which is a two, three and 4-lane road. Good road, very driveable. It then will take you into Jonesville, VA and from there, I haven't driven it, so I can't tell you anything about the highways.
(If you are looking for somewhere to stay around the intersection of Rt 23 and 421, Natural Tunnel State Park is great and about a mile off the highway.)
Hope this helps. We do have mountains around here and there is no way to get to Harlan from Florida that you won't have to go up mountains.