Well, since her husband died in 1864 OTL, he was likely still alive since the CSA won their independence probably by 1863 since the battle that secured CSA independence was in 1862. That would explain why the Patton family would still have stayed in Virginia. If we use that as a base, we can also assume that because General Billy Mitchell was from a Northern State, whose father fought on the Northern side of the war, it is likely that his family stayed in the US. I can't see a reason why he would go south, especially being on hte losing side of a war.Patton's Grandmother moved to California after her husband was killed during the Civil War, so Patton himself is two generations removed from the CSA. Even if his grandmother hadn't moved his father might have during the period between the War of Secession and the Second Mexican War, before the CSA had a Pacific Coast.
and it's kind of hard to find an appropriate photo to represent a fictional person, especially one symbolizing such a significant role X) This is meant to symbolize "real" people who might have ended up serving the CSA.
For Nathan Bedord Forrest III, he was a real person. Just look it up on the turtledove wiki and wikipedia: