L.B.
I'm originally from Mobile, and make this drive a few times a year. Unfortunately, there isn't (in my opinion) any "must see's" along the way. We have made detours to New Orleans to take the kids to the Aquarium. There are also swamp tours and LOTS of historical home tours - but other than that my only other suggestion would be Battleship Park. It's actually not in Miss as stated below, it's in Mobile, Alabama. My boys are 6 and we took them this summer. They had a blast on the ship and submarine, and there is also a flight simulator. You could also drive to Dauphin Island and take the ferry across to Fort Morgan. More... historical forts, etc. not really a lot to see but a break for the kids. Google Mobile Bay Ferry for information. The coastal drive to Destin is nice too (but LONG!)
I guess it all really depends on which way you plan on going.