I don't think it's a good time to travel.
You should be well prepared if you want to safe in this trip.
I will try to find a few links about you should know about travel and post them.
https://www.nafsa.org/regulatory-information/covid-19-restrictions-us-visas-and-entryJust make sure Park opening time before you go there.
Visit follow site for camping in Arkansas
ArkansasStateParks:
Woolly Hollow State Park :
http://www.arkansasstateparks.com/http://www.arkansasstateparks.com/
Petit Jean State Park
:https://www.arkansasstateparks.com/parks/petit-jean-state-parkMississippi River State Park :
https://www.arkansasstateparks.com/parks/mississippi-river-state-parkMeeman-Shelby Forest State Park: https://tnstateparks.com/parks/meeman-shelby
Chickasaw State Park :
https://tnstateparks.com/parks/chickasawHenry Horton State Park
https://tnstateparks.com/parks/henry-hortoncamping for kids in North Carolina
Stone Mountain State Park:
http://www.ncparks.gov/Hunting Island State :
southcarolinaparks.com/huntingisland/introduction.aspxMaby rent a RV is a not bad idea for you.
Unavoidable access to people by public transport.
https://www.storyrv.com/ is a site about RV trips.
Please be sure to wear a mask..
Good Luck