SWA is one of the only airlines with which this will not be a problem, as they will give you full credit for what you paid for the flight if you cancel or make any changes. That's in the form of a credit for future flights and not an actual refund, unless you have purchased an unrestricted fare. You just need to pay the difference in fare if the rebooked flight costs more or you get an additional credit to use if the new fare is lower.
If you expect that only one of your parents will need to make changes, then booking two separate tickets probably is the best way to go. Then you can just cancel and rebook one ticket instead of both. Otherwise, you would have to cancel and rebook BOTH tickets and pay any difference.