When you checkin, online, at that 24 hr window, you will get a boarding group number. This is basically how that works.....you will see a letter, A,B, or C..most likely A or B. Within that group you will get a number. A group starts with A16. A1-15 goes to business select fares, and fully refundable fares. Medical preboards and minors flying alone will board before the A group.
So, those with EBCI will get checked in, by SW, 36 hrs before the flight. They are checked in according to when they bought EBCI. Then, those checkin in at the 24 hr window can get their spots. With a 3 y/o, you will be allowed to board, no matter what your boarding group assignment is, in between the A and B groups. Now...the only thing that I can't be absolutely sure of is this...if EBCI people take up the entire A group, and go into the low B group, I'm not sure if families are allowed to board before those with EBCI B group. But, that probably isn't a huge issue.
So.....when you get to the airport, you will see lines, with poles with A, B or C on them (they flip them around depending on which group is boarding), and withing those letter groups, poles with 1-5, 6-10, 11-15 and so on for each letter group. You stand in the slot you see on your boarding pass. Those with B groups will remain seated, at the gate, until the A group is boarded. And so on. Those with children under 4 will be allowed to board after the A group.