Based on the information in your signature you don't qualify for family boarding since your children are over the age limit.
Re: EBCI, those who purchase EBCI are checked in automatically 36 hours out and their boarding position is assigned based on when they purchased EBCI. Your ticker indicates you have a trip in just over a week. If you are flying Southwest on that trip, I'm not sure it's worthwhile to purchase EBCI at this point. Purchasing it this close to your travel date is going to put you at the end of the EBCI line unless you purchased an Anytime fare and EBCI in which case you would be ahead of those who purchased Wanna Get Away fares plus EBCI.
It might be worthwhile to purchase EBCI now if you cannot be online at EXACTLY 24 hours from departure to check yourselves in for your flight so that you can secure the best possible boarding position.