SWA's current policy is that only single-ticket itineraries are eligible for online checkin. If you have more than one person on the reservation, you cannot print boarding passes at home, you have to wait until you can use the kiosks at the airport.
If you are travelling with children who are over age 4, there is a chance that if you wait until you reach the airport to get boarding passes, you may all get "C" passes, and on popular Florida routes, that may mean that the family will not be able to find seats together, on even, sometimes, 2 pairs of 2. If you are travelling with a child who is 4 or younger, you can normally preboard, though SWA can suspend that right if there are a lot of kids on a flight. Carrying a carseat on board for a child under 40 lbs. will guarantee that at least one adult and one child will get to preboard at all times.
My personal belief is that SWA is sticking to the one-person-per-itinerary rule because most itineraries of that type are business travellers, who usually pay walk-up fare. They want to entice them by giving them first choice of seats.
I do the separate tickets by opening that many simultaneous browser windows, and cutting and pasting the payment info between them.