Some airlines are equipping newer planes with power ports, but SWA isn't one of them, as far as I know. In any case, as someone else noted, it is not the sort of cable you can use in a car; aircraft power port cables are different.
However, here is a tip re: keeping the batteries charged. Depending on where you fly from, the gate area may have power outlets, so try to get a seat by the wall, and you may be able to charge your battery right up until you stand up to get on the plane.
On the plane, keep the DVD's for last; don't turn it on as soon as the seat-belt sign goes off. We always let DS have a meal on board; he knows that as soon as that bell dings, it's munchie time. (We let him have an otherwise forbidden Lunchable if we are on a plane.) That's good for 30 minutes, usually, and there are other possibilities as well.
Oh, if you have two kids who will be listening to the DVD, see if you can get the headphones that don't have a band; where each earpiece is just on the end of a soft wire. Two kids can use one set that way.