Jacksonville FL to Pigeon Forge TN to Evansville IN

If possible, try to limit yourself to 4 or 5 hours a day driving. Yes most folks can do more, but to make the trip less stressful 5 hours is a nice easy number. The interstate route of 530 miles is an easy 2 day run. 95 to 26 to 40 to 411 .
As to mountains, are you pulling a toad? Interstates tend to have fewer really steep sections than secondary roads, but are also less interesting as far as things to see and do.