I think they've both spent enough time in mississippi to account for the accent. As for their time in New Orleans, I don't think you'll find it very common for someone who is a "1st generation" new orleanian in their socioeconomic bracket to have that "new orleans" accent these days. To sum things up, here are my reasons that they don't have a yat accent:
1) First things first: not that many people who go to Newman, et al. have any distinguishable new orleans accent. Having gone to Ben Franklin, and knowing lots of people from Newman, Country Day, St. Martin, etc, I'd say far fewer than 10% had a heavy accent (to my ear, anyway).
2) If you're a 1st generation New Orleanian (your parents grew up somewhere else), you're not likely to pick up that much of an accent even if you spent a lot of time in New Orleans.
3) They spent a lot of time in Mississippi, and their dad sounds just like they do...hmmm