It's not a crazy or too onerous drive, but I must ask why Atlanta? Are you visiting Wasington DC or Wash. State first? What are your interests?

DC, and the timings dictated we must fly on Easter Monday, so flights to Atlanta were best value and the only direct ones. We wanted to incorporate a drive into the trip anyway, we don't plan on spending any time in Georgia, but rather get straight into Alabama. The kids are crazy about space and science, so we considered Hunstville, but we're doing the Smithsonians in DC and Johnson Space Centre in Houston so they've got quite a lot of that already, and Huntsville seems rather out of our way. We all like outdoor things; walking, cycling etc, and the other half loves the Southern food and music. I've heard good things about the Natchez Trace Parkway, but again this seems slightly out of our way. We'd make the extra miles to do it though if its worth it; we'd prefer a scenic route rather than Interstates all the way.

Thanks for your reply!

Of many parts of the country, the "scenicness" of this drive is NOT it!! Sorry to say.
Go to NOLA and enjoy it, and then just drive.
Montgomery has the Civil Rights Memorial at the Southern Poverty Law Center.

If you are intersted in a beach day, you have several good opportunities. Destin, FL; Santa Rosa Island; Gulf Shores, AL are all popular destinations.

If I had a choice, I'd actually do my driving in Virginia and North Carolina, perhaps renting a car right in DC and returning it to either Dulles, Baltimore, or National airport depending on the flight and then flying nonstop to Houston. That is unless you really truly want to see Alabama and New Orleans. Or I'd fly direct from DC to New Orleans, as Gretchen suggests, and then do the driving.

But I also can't really recommend the drive from Atlanta. Look into flying into Memphis if you really want to start somewhere in the south.

I'm assuming you've already figured in the huge cost of a one-way car rental.

Thanks so much for your replies. Yes, we would really like to see Alabama, Mississippi and Louisiana as we've never visited these states before. The car hire one-way fee is extortionate, but not as high as flights into New Orleans. At the moment we're thinking of driving straight to Birmingham, AL, spending half a day there, then driving on to Jackson MS for a night/day. We could then pick up the Natchez Trace Parkway for a day, before driving on to New Orleans for a day. The 5 hour drive from New Orleans to Houston we'll just blast through on the last evening. As Brits abroad, we'd like to experience the food and culture of the south as much as possible.

I'd give Jackson MS a pass unless there is something in particular there you are looking at. Natchez MS or even Vicksburg MS would likely be better choices for you.

Another option you should consider would be the Amtrak Crescent #19 which leaves Washington DC at 6:30 PM every night. It goes through Atlanta and arrives in Birmingham at noontime (Central time) ~18 hours 20 minutes. The coach fare for 2 adults and 2 children under 15 would be $480.
Rent a car in Birmingham and see what you want to see in Alabama and get on the Crescent the next day to go into New Orleans.