No - SWA uses "ticketless travel" but you can print your e-mail confirmation or Itinerary, I do it just for reference.
Then 24 hours prior to your flight time go online and check in to help getting A group boarding passes. You can print them at home and bring them with you or wait and have them printed at the airport.
At the airport if you check in via curbside or inside at the desk all you need is your photo ID and that of anyone traveling with you that is 18 or over. If you use an automated Kiosk you will need your confirmation number.
I just noticed your triplets are 4 in which case you will be allowed to pre-board. Medical preboards will board first and then families with children 4 and under board first come first serve. (And believe me they do line up in the preboard line??)
TJ