Technically SWA does not have to let the older children board with you, but IME the letter of the rule and the rule in practice are normally not the same.
I fly SWA frequently, and in practice I have never seen a situation where a nuclear family consisting of one adult and multiple minor children was told that some of the children would have to wait and board separately as long as at least one child was no older than four. I've never had a GA deny my DS the opportunity to board with DD and me, even though he is taller than I am -- he's 14 and looks it.
If there are two adults travelling in the party, then yes, I've seen the older kids left back with one of the parents if there are lots of families on the flight, but when only one adult is present, my experience has always been that any kids who are obviously too young to drive are going to be allowed to preboard with their parent and sibling. Older teens perhaps not.