As long as the second flight you want to change is a valid routing with your first flight, you should be able to SDC to your wife's later flight out of ATL within 3 hours of your first flight, so you won't even have to deal with a GA.

So if this fictional itinerary was for you + wife:

You
09:00AM AAA->ATL
12:00PM ATL->CCC

Wife
10:00AM BBB->ATL
04:00PM ATL->CCC

You should be able to call and SDC your second segment at 6AM.