Perhaps one of Spanish America's failings in the late 19th Century was that it lacked a Bismarck or Bismarcks. Argentina did well in the 19th Century. Argentina was able to attract several million European immigrants in the 19th Century. But Argentina, for all of it's success was not able to unify the Southern Cone (Argentina, Paraguay, Uruguay, Chile, Bolivia, even Peru) into a nation that could hold it's own with and stand up to the United States. And by the beginning of the 20th Century, in Latin America, that was what was necessary.
An Argentina that could take over the Southern Cone and Peru (or even Brazil, conquering all), a Colombia that reconstitutes Gran Colombia by retaking Venezuela and Ecuador and then perhaps Central America all the way to Mexico by the late 1880s, all of which providing the United States with a fait accompli by the time the US is strong enough militarily and economically to look beyond it's borders; that is what is necessary for Latin America to meet the challenges of the 20th Century.
And that is the best we can do in this pre-1900 section. Other South American TLs could work, in which, for example, a Sweden that rules Norway provides the UK with real competiton and either establishes colonies in Southern South America or displaces Great Britain into establishing colonies in Southern South America. But then these areas are not Latin America, are they?
The most serious issues Latin America had to face must be addressed in the post 1900 section since they involve the role of the United States in perpetuating kleptocracies, dependence on commodities and the cheap labor to extract them and continued underdevelopment in Latin America. Development in Latin America can, in many ways be seen as something that has occurred in spite of US policies in many Administrations designed to prevent it. But that's a matter for Post 1900.