hulabird
there have been various posts on the boards that say there is no problem calling SWA to separate into single confirmations for each one in your group
but, sorry to say hulabird if you have special fares ( eg youth fares ) you probably will not be able to check in on line for those fares
from the SWA website ...
To use Online Checkin @ southwest.com and print your Boarding Pass, you must:
Check in beginning at 12:01 AM local time day of departure, up to one hour prior to departure
Have a single-passenger, Ticketless reservation
Be checking in for flights that have not already departed
Have purchased an Adult fare type (Customers holding reservations for group, senior, infant, youth, or military fares, and those requiring an additional seat must proceed to the airport for checkin)
if the kids tickets are actually adult fares purchased onsale, then you should not have a problem