Hey Pup!
I just did that exact trip this past summer. This was a first time camping experience in our brand new 20' Conquest trailer. I live in Bluffton, SC so I know exactly what you have in mind. I am planning on a trip to Glacier this coming summer and feel totally confident about the drive times as I drive on my own with my son keeping me entertained, for the most part. Driving by myself, the average daily drive distance was about about 350 mi/day. I've learned time can be irrelevant as some miles are simply easier to go than others...especially when the scenery is vast. Anyway, it is pretty much the exact same trip, only I've decided this time to head up into ND.
This was my route to get to the Badlands and Black Hills along with my campground recommendation:
Bluffton, SC > Cartersville, GA (Lake Allatoona Marina Campground - very friendly)
Cartersville, GA > Paducah, KY (Fern Lake Campground was a nice stop)
Paducah, KY > Colombia, MO (Cottonwoods RV Park - very nice campground, all pull through sites)
Colombia, MO > Omaha, NB (Lake Manawa State Park, dry camping w electricity and gorgeous lake - stayed 2 nights and went to the Omaha "Henry Doorly" Zoo - FANTASTIC!)
Omaha, NB > Oacomo, SD (Oasis Campground - overlooks MO river. Liked it so much we stayed there on the way back!)
Oacomo, SD > Badlands Nat' Park (slim picking for accommodations, but a jewel in the dirt > Badlands/White River KOA - great for kids, absolutely loved it! Stayed 2 nights - Prairie dogs will steal your hearty and they, along with the Mtn goats, are everywhere!)
Badlands > Hill City, SD (Here, I could go on and on. The Black Hills are simply sumptuously amazing!!! We stayed at the High Country Guest Ranch as my mother had a cabin and they have spots for rvs. They have a huge stage where an Amer Indian troupe perform almost every night, horseback riding and more. Centrally located for 5 days of road trips covering every sightseeing" loop. Fell in love with Custer Nat'l Park where the Bison and Buffalo roam around your cars.)
We allowed for 2 days in Badlands (though y mother was there for 4 and loved it) and 5 days for Black Hills. If you do the Northern Loop to Deadwood, make an early start of it and go on out to Devil's Tower Nat'l Monument in WY - absolutely fascinating!
If you want more recommendations, let me know. I fell in love with SD. So, I am willing to see what ND has to offer on this next trip.
Samantha