I believe that as long as you have a confirmation # you can check in 24 hours prior to your flight. Although if the kids are young enough (5 or younger but not really sure of the age) you get to pre board before anyone else.
As long as you have not booked children's fares (you have to call for these) you can check in online. You might want to read this: http://www.southwest.com/travel_center/retrieveCheckinDoc.html#requirements
Even if you have children under 5, it is a good idea to checkin online, as sometimes they do suspend the preboarding for families with children under 5.
I believe that as long as you have a confirmation # you can check in 24 hours prior to your flight. Although if the kids are young enough (5 or younger but not really sure of the age) you get to pre board before anyone else.
They do suspend preboarding for children under 5 if there are too many pax with children. It is always wise to check in online regardless of the ages of your children.