That would, of course, depend on the Roosevelt boys not being broken (mentally or physically) or outright killed in the Great War - a dangerous uncertainty, given these chaos would have been ‘in harness’ at the hour of their nation’s bloodiest exertions.
It also rather depends on them not having been so overshadowed by their mighty father that their own reputations were able to flourish (Quite difficult to guarantee, as we may observe from the fact that in almost two & a half centuries only two fathers have seen their sons follow them as President of the United States).
Yeah that might be Difficulty with President father and son things, but I think Teddy sons still have Change of the Presidency.
When the Freedom Party want to Remilitarizes and be Aggressive to the Union, peoples will want a Person when Shit get Real with the South.
What will be a Better Person, then the Son of an President who drive the South to it’s Knee.
Plus Teddy sons (my money is still on Quentin Roosevelt as President) might Popular as or Even more Famous than their Father
because No President of Southern victory never did before….. . .. . . .
Permanently Ended and Reintegrate the South to the Union.
Which whatever Teddy Sons as President Popularity will be Enormous after the War and Put him to Best President’s in American history.
Also in the Story standpoint, the Son finally out their Father shadow and makes their own Legacy separate to being just son of Famous Man.
That will be Amazing Character arc to explore if Southern Victory has Adaptation