We fly out of Kansas City and I find Air Tran to be fairly expensive. The best low cost options are Southwest and Delta. We've flown both, but Southwest is the only one of the two with non-stop flights.
With that said, do Southwest. While there is no assigned seating, it's generally not a problem. There are three possible boarding assignments, A, B or C. The A group boards first, followed by the B group, then C. It's easier if you have an A pass. The easiest way to get one is to check-in exactly twenty-four hours in advance of your flight. For the flight home, go to Guest Services at any park exactly twenty-four hours before the flight home and check-in. They will print your boarding pass for you. Disney hotels will do this too and I'm sure other non-Disney hotels will as well.
However if you get a B or C pass, it's still not a problem. The airline personnel do try and make sure that kids sit with at least one of the adults taking them on the trip. On our last Southwest flight, my husband sat with our two girls and I was sitting in a seat behind them. A dad had a C pass and was disappointed that the seats left didn't allow him to sit with his son. I promptly got up and moved, volunteering the seat I'd chosen. (The seat next to me was empty, so my moving freed up two seats next to each other.) If no one volunteers, the staff have been known to sweeten the deal with free adult beverages.
As for Delta, we've flown them before and did so this summer. It's fine and while it is a hassle to go through Atlanta, it's doable. The kids you're taking are old enough it shouldn't be too big of a deal. Ours think the "subway" in the Atlanta airport is pretty cool! My biggest complaint is the time it adds to your flight, but we didn't have any other issues.