All Southwest planes are 737s with three seats on each side of the aisle. Unfortunately, that means that all four of you won't be able to sit exactly together no matter what. Someone can sit across the aisle, however, which is very close.
If at least one of your children is young enough (4 or under, I think), your entire party should be able to pre-board and you won't have any problem getting your choice of seats. If they're older, the trick will be to get the 'A' group boarding passes so that you're in the first group after the pre-boarders. To do that, you should check in online exactly 24 hours in advance of your flight departure time. You can print your boarding passes out then or wait and get them printed out when you get to the airport. It really doesn't matter. The key is the checking in part, not when you print your passes.