Southwest does not have assigned seats and you board in order based on a number assigned at check in. Passengers with medical pre-board clearance and unaccompanied minors board first, then A1-A15 board next with those numbers reserved for elite frequent flyers and passengers who have purchased a higher-priced Business Select ticket. Then, A16-A60 board followed by families with children ages four or under. After that, B1-B60 board followed by anyone in the C group.
If you do not use EBCI, you can check in online starting 24 hours before your flight to get your boarding number assigned. Generally, that will get you in the A group and even if you get numbers in the B group you typically can find seats together. In your case, a B pass could mean that you'd have to split up into a group of two and a group of three, but wouldn't mean that your kids would have to sit alone.
If you use EBCI, however, Southwest will check you in automatically 36 hours prior to your flight time. While that will not guarantee an A boarding pass, I have only read one report of a passenger using EBCI getting a B pass and that was for a flight originating out of Chicago Midway, where SWA does a lot of flight connections.