You can take the car seats on the plane, but they have to go in the window seat, so you may have to sit in 2 different rows. Make sure you ask SW about side-by-side car seats; don't know their policy for a parent traveling with 2 in seats. Car seats can be checked as luggage at the counter and DO NOT count against your bag limit, which is 2 each on Southwest. Some kids are used to being in their car seats (mine aren't), so it may be easier and less stressful.
Also, SW doesn't do early boarding anymore. Family boarding is between the A & B boarding groups. Try to check in 24 hours before your flight, and you should get an A, which will give you better seat selection and more time once you get on the plane.
I personally think car seats aren't worth it, and I know it's been said that's it's safer, but have a discussion with your twins for a few weeks leading up to the trip that as long as the seat belt sign in on, they have to be in their seats with their seat belt on. Not taking the car seats gives them a little room to move around and play with whatever toys you take with you while they're allowed to be up and around.
My son has been traveling since he was 7wks, and as soon as he was big enough, he wheeled his own "pack pack" through the airport with the toys he decided he wanted to take. I know we travel quite frequently, but he even knows when he's allowed to get out of his seat. Flight attendants (especially Southwest... we LOVE SW!!!!) don't usually have a problem with little ones being out of their seats to play as long as they stay in the row. I let my 3.5yo take a walk every hour, and most flight attendants just love to watch him. I make sure he's not in their way for servicing, and he's not allowed out of his seat if it's rough even if the seat belt sign isn't on.
Another tip would be to start packing about 3-4 days before you're leaving and try to be completely packed with luggage by the door the night before you leave. The only things you'll have to worry about the day you leave are the stuffed animals the kids sleep with, etc. We also travel with a food bag with snacks, etc, and our DVD player ALWAYS comes out! A lot of traveling is what you make of it and how prepared you are ahead of time. Have fun!