It'd probably alter in 1932 with Butler being injured when federal troops cleared the Bonus Marchers. They decamp but reorganize as a national movement, supporting FDR in the elections. For this reason the Business Plotters do not try to use veterans to forcibly gain control of FDR but instead through bribes and political capital insinuate themselves into FDR's life and gradually weaken him with slow poison while restructuring the cabinet around their cronies and bought men. When the Bonus Army returns to Washington demanding to see FDR in person, there is an armed conflict with federal troops. Following this incident VP Garner and those in Congress who believe that the President is dead flee the city while they can, bringing those troops loyal to them to a new provisional capital at Austin.
With both governments lifting prohibition and "communists" (both the actual Reds and the Bonus Army) "trying to take over", the temperance movement and Depression era evangelical resurgence blossoms into the Temperance Army.
The Red Army is of course an opportunistic entity, the International Brigades to the Bonus Army's Catalan Workers, just with the positions of strength reversed despite Soviet aid to the Reds.
The Bonus Army does eventually take D.C. but the Coup Government removes to NYC and the burning wreckage of the former capital is recaptured by Federal Troops (I'll use Loyalist Troops for those answering to the Garner government) using tanks soon after. The strategic leadership of the BA allows them to remove various artillery pieces from the D.C. defenses and carry them even in retreat. Having endured a massive lost of manpower they draw new recruits and begin training from a defensible area (any suggestions?).
If the thing drags on the Business junta will make an alliance with Germany while Cactus Jack will do the same with Britain, for all the good it will do either them (The Austin Government or Britain, both heavily preoccupied in separate arenas). Practicality might make the Garner Government deal with Japan rather than Russia (who is able to do more for the Western U.S.? Or in other terms, Garner would rather not have to worry about Hawaii being invaded while fighting for half the country and isn't predisposed to like the USSR when it has given at least some aid to rebels within the US).
A list of the players in this civil war, to sort things out:
United States of America (Coup Government, Federal Troops), capital NYC, NY
United States of America (Garner Government, Loyalist Troops), capital Austin, TX
Bonus Army
Red Army
Temperance Army
Maybe Britain and Russia hold out by the skin of their teeth until Germany implodes as one leader after another is assassinated, halting any further expansion attempts. This leads to the Business Coup junta being deposed but the second USA remaining a separate nation due to the threat of the Bonus Army. Without being pushed to craziness the people of the Eastern US restore a truly democratic government but a few decades later a revival movement institutes the trappings of a board of directors serving on an a outside-the-cabinet super-council.
The Red Army and Temperance Army fizzle, Garner's Western US stabilizes and the martial law ends by popular demand. The Bonus Army officially disbands though it's influence as a political movement remains in the Western US for decades and just as long in the Eastern US as a "communist" boogeyman in popular culture.
Garner country remains the United States of America while de facto and eventually officially the other one becomes the United Federal States of America (UFSA), nicknamed the FSA by non UFSA citizens.