I’ve travelled from Nashville, Memphis, Clarksdale, Vicksburg, Natchez to New Orleans - you could obviously do this in reverse.
New Orleans is a great city with lots to see and do. WW2 museum as others have said, garden district, riding the streetcars, cemeteries, ghost walks, swamp tours, Segway tours, lovely streets to wander around, drive out to a plantation. There are plenty of nice places to stay, but I’d probably avoid Bourbon St as it will be a bit on the rowdier side.
From there head north on the Natchez Trace Parkway passing through Natchez, Vicksburg & Clarksdale towards Memphis. Maybe stay a night in the Shack Up Inn.
Spend a few nights in Memphis. Go to Graceland, Sun Studios & the fantastic Civil Rights Museum. Eat fried chicken at Gus’s and BBQ at Central BBQ. Go see the Peabody Ducks.
Nashville is also amazing but I spent a lot of time in the honky tonks, not sure if they allow children at any time but still lots to see & do. Go see the Grand Old Opry, visit Bluebird Cafe, Country Music Museum, spend some time in 12 South area.
From Nashville you could head east towards Pigeon Forge & go to Dollywood, spend some time in the Smoky Mountains.
Then north towards Louisville, Ky before heading to Chicago.