We (4 of us) always try to travel nonstop. Since you are traveling in October, there is always a chance for bad weather, so I wouldn't pick a non-direct flight. We have mostly traveled with SW and never had a lot problem picking seats together. However, it can happen. If you are so worried, you should pick AirTran $144, so that you can pick seats.
OP's concern is that it's technically an AT flight but when it's booked through SWA, you can't choose seats. If she books same flight directly through AT, the price goes from $123 to $144 plus the cost to reserve seats.
OP, I also have a 16 yr old though he's flown often but we still like to sit together. Usually I don't mind paying extra for the seat selection.
If you chose the AT via SWA route, and you don't get to sit together, how stressed out would you be? Would you then be willing to pony up the extra $$ to be together? If so, you have your answer.
I never fly Delta simply b/c they don't fly non-stop from Philly but I do hear often here how they change flight schedules often. changing times, non-stop to a connecting flight, etc.
Also it's helpful to others if you keep in mind the flight terminology so everyone knows exactly what you mean, and the airlines too if you call with questions.
A direct flight isn't necessarily a non-stop. It could stop somewhere but you don't have to change planes. Not a biggie to many but if you have fear of flying or not good with take offs/landings, etc you may want to limit your search to non-stops. They minimize your overall time door to door.
A connecting flight is one where you have to deplane & go to another gate, then get on another plane. Though you don't have to retrieve your luggage for the 2nd leg, it does increase the risk your luggage could be delayed/misdirected. Also if weather is bad, not just in your home town, but even just fog in the city "your" plane is coming from, it could delay your 1st leg & cause you miss your connection.
Long story short, go for a non-stop.
