Which part of AL? I just drove from AL to WA last Fall, are you going to go I-90 to Sioux Falls and then South to Kansas City and then into Nashville and South on I-65. It's an easy drive, maybe not this time of year, but half the trip is I-90, it's over 1000 miles from Seattle to Sioux Falls alone.
OK, the cats will be insane and probably howl the entire way. Every night in hotels they will wander and try to get out and keep you up all night. I would not wish 3 cats moving like that on anyone else. Pack a bag of disposable gloves (Lysol makes a canister of 50 pairs, BTW), wal-mart bags, old towels for lining the kennels, baby wipes and lysol wipes because if your cats are like mine, they will puke and crap their neurotic asses off across the country. If any of them have medical issues, hand carry their vet records. My cats were in a kennel in WA waiting for us to get back on our drive, thankfully. I wish you luck there.
You're not going to be without your stuff for long, just take anything you might need for the length of time. Any personal (BC's, SS cards, all that stuff I never ship and always had carry) and financial documents and I would just hand carry any ammo or anything they won't ship. Keep your copies of the shipping info, stuff like that. Honestly, you won't need much. Just fill a file folder with your crucial stuff--utility info from your current home in case there is a problem later and you need to contact them, banking statements, everything the movers give you, car stuff, etc. You think about it a minute and you'll know what you personally might need there.
I brought my cleaning solutions from TN to GA in a bag in the back of the truck rather than throw it all away because I'd just be buying it again the second I got there. Also, pack a mini medicine cabinet. Carsickness meds, antacids, tylenol, diarrhea meds, etc. Oh, and chapstick, we practically went through a tube of chapstick in 3 days between the 5 of us. All that road tripping makes for upset bellies and gas from crappy fast foods and that shit is expensive at gas stations. I'm an over-preparer, though.
I also had a soft-sided cooler that I kept stocked with bottled water and tea. I would buy sandwich stuff as we went or cheese sticks and fruit and stuff like that for snacks. A little planning will save you a buttload on the road.