[*]US invades Brazil ( I am still trying to find a reasonable realistic reason)
And there's why this seems like an alt-history story, not a future history story. A reasonable explanation as to why the US would want to invade Brazil does not seem to exist. And if the rest of your story depends on an unreasonable initial condition, the rest of the story is shaky at best.
Alt-history explanations:
1) Brazil went full commie/Soviet vassal state in the 60's. Soviet Union never collapsed; World War Three finally kicks off, starting in Brazil for some reason.
2) The US Civil War ends with a CSA victory, at least insofar as the CSA survived as an independent nation. However, the rest of the territories of the US end up as US states, leaving the CSA as a small, angry little nation surrounded by a larger, more powerful enemy. As the CSA economy recovers from the war, The CSA turns southwards, conquering Mexico in, say, the 1880s, and slowly marching south, eventually conquering all of South America. By the 2020's the CSA is a vast empire, now with its capitol in Brazil. The USA and CSA go to war again.
2A) The same initial setup, but it takes until the 2020's for the CSA to get to Brazil. It's not the USA that invades Brazil but the CSA.
Second thought... a possible explanation why the US invades Brazil. Taking Afghanistan/Iraq as inspiration: Venezuela gets hold of a couple nukes (old Soviet? new Chinese?). As a way to divert the Venezuelan people from the continued economic disaster that socialist policies created, the Venezuelan government blames the phantom of eeevil Americans. As things continue to spiral, the Venezuelan government gets increasingly paranoid and crazy, and eventually sets off one of their nukes on US soil for reasons best described as "bugnuts." The US decides that that merits a full invasion of Venezuela; the Venezuelan government flees to Brazil and the Brazilian government refuses to hand them over to the Americans. The US then invades Brazil to grab the Venezuelan politicians responsible for the deaths of thousands of Americans. the Brazilian government in this scenario would be objectively the badguys.