Nice Chapter Antonio, I like how this world is taking shape, but again a couple of caveats:
1.- Until 1929 Chile was still occupying Tacna, and only let it go back to Peru after Heavy USA influence, so if Brasil Take over Peru before 1929 There is little reason from Chile to Let it go Tacna
2.- Even as the Uruguayan and Paraguayan Invasion is relative Easy for Brasil, I Doubt they Could Take Over Bolivia alone, for a Logistic perspective Alone, basically Bolivia don´t have any infrastructure worth the name and /or navigable rivers outside the Santa Cruz de la Sierra, Beni and Pando departments, so the Take over on the Altiplano where lived the most of the population, is a really difficult proposition at least from the East, from the West, from Chile is Easier as Chile because the Pacific war Treaty build a Arica-La Paz train, That start their operation on 1913, and is still functional in the Chilean side, but you say Brasil fight the war alone, and to make the situation more difficult the Altiplano is so over the sea level, 3.700 meters in average, that the altitude sickness is really bad if you don´t take a long acclimatization period.
3.- The same apply to Peru, The Peruvian Altiplano, the so called sierra have little to none infrastructure an to make the thins more difficult, the brasil-peruvian frontier even today is little populated and in the worst of the amazon jungle, the most green, full of sickness place on the amazon, and almost all the important cities in Peru are in the Sierra or the pacific coast, and Peru don´t have a fleet worth the name until 1940, so the best invasion Ways are from the North From Ecuador, but Ecuador don´t have and army capable enough to take over Peru alone, from the Pacific on ships, difficult proposition the only ways are the Panama Canal, that by international treaties can´t let war material pass, and the Horns cape or drake passage, that are in hands of Chile and Argentine navies, that where at the same power that the Brasilian one, they where recently in the end of the
South american dreadnought race, and from the South from Chile as Chile build train infrastructure in Peru as part of the Pacific war treaties, But again you say Brasil only have the support from Ecuador.
Well my point is The Brazilian invasion over Peru and Bolivia, will become Easier if Brazil allied themselves with Chile and Ecuador to do a partition of said countries
Either way Brasil will have a long a costly Guerrilla independent warfare from Peruvian, Bolivians, Paraguayans and Uruguayans, as most of these countries have a long history of guerrilla to maintain their independence, and the Brazilian population is not that bigger than the conquered territories, 27 million vs 13 millions (7 of peru, 4 of bolivia a million from uruguay and another million from Paraguay)
here a map of the political situation in 1920, with a slightly larger Chile