I have a Jayco 28bhsw TT and a 2500HD. Traveling with wife and kids, 2 and 5(they're troopers, trust me). I'm hitting a friend's place(private campground) near 76 falls in Lake Cumberland heading sout...
The Blue Ridge parkway is one of my all time favorites drive. Beautiful overlooks, nice road, and very doable hills and grades. Campgrounds are exceptional with the exception of Peeks of Otter. Check it out at www.nps.gov/blri
By the way, I found the Biltmore to be expensive and not worth it. I think it will be a complete bore for the kids and they and you will be miserable.