The general idea of a full unify latam/hispanic is a pipedream, from ancient communication means(would take telegraph for realtime communication and full fledge steamships just to decent travel times) but the idea of a latin america coordinate as a block would need to start with 1810(Miranda first independentist junta in april and them the rebellion in july and mexico scream) with more coordinates indepenentist group and one can achieve a quick one, so for 1815 and before nappy I is defeated, we've a fully independant continent(the carribean can come...but is possible for Cuba, PR and Dominican republic too) and full fledge nation like Empire/Republic of Mexico, Centroamerica republic, (Grand) Colombia, Peru, Bolivia, Chile and La Plata(Argentina+Uruguay...maybe more of soth brazil too) alongside paraguay, and them coordinate common policy to keep spanish out and avoid meddling of USA fillibuster in the future.
With all due respect, I must disagree. You don´t need such an earlier coordination as 1810, and anyway at that time the independence movements could not take advantage of such coordination: before they can help other movements, they must agree among themselves, and defeat the loyalists of Spain in each of their regions. OTL, the closest movements tried to help each other, with diverse results, but a coordination of all simultaneously is also a pipedream. The distances, the internal divisions between centralists and federalists (La Patria Boba in New Granada, Buenos Aires vs Montevideo), the different natures of the movements (Hidalgo and Morelos movement compared with the Juntas in Venezuela or Argentina) and the closest royalist menace, also we can´t forget the unfavorable international situation (at that time Britain supported Spain, as its ally against Napoleon and did not suit to their interest the weakening of such ally, until the Corsican ogre was defeated). Instead, you could achieve the same result that you search, with a succesful
Amphictyonic Congress of Panama.
Precisely, Simón Bolívar organized that congress in 1826, with the objective of bringing together the new republics to develop a
"common policy to keep spanish out and avoid meddling of USA fillibuster in the future", and for that, he also proposed creating a league of American republics, with a common military, a mutual defense pact, and a supranational parliamentary assembly. The Liberator invited all of the Hispanic America independent governments (and Brazil), but only was attended by representatives of Gran Colombia (comprising the modern-day nations of Colombia, Ecuador, Panama, and Venezuela), Peru, the United Provinces of Central America (Guatemala, El Salvador, Honduras, Nicaragua, and Costa Rica), and Mexico. Chile and Argentina were not interested (they distrusted the Bolivarian project and feared that this would mean the beginning of a Gran Colombian "hegemony". Also Argentina was distracted with a War with Brazil over Uruguay), Brazil did not attend (because they thought they would receive a hostile reception there due to the war with Argentina), Paraguay rejected the invitation (because its dictator, Dr. Francia, was a firm believer in isolationism) and Bolivia did not arrive on time (political struggles caused delays in the appointment of delegates).
Unfortunately, among the countries that did attend, only Gran Colombia ratified the agreements reached in Panama, the idea of continuing the Congress in Tacubaya (Mexico) did not materialize, and the combination of internal tensions, mutual distrust and political struggles not only did prevent further unification, but ruined existing attempts: Just 4 years after Congress, Gran Colombia had dissolved.
If all the invited countries had attended, and if all had ratified the agreements, either in the terms of Bolivar or those more limited that were achieved in Panama OTL, the region would have advanced a lot in integration. But for that it would be necessary that the leaders of Hispanic America had the same firm belief in that "grandiose idea"; that the regionalist tendencies of local elites who did not want to have anybody over them after being free from Madrid, of "caudillos" who preferred to be first in their village rather than second in Rome, were overcome.
The rest is the biggest i can imagine, Maybe Peru+Bolivia not collapse and become an indigenous based nation, Chile could sign a mutual alliance with argentina with chance a federation, ditto paraguay, but the rest is hard to pull
I don't want to be negative, but to get a federation of Chile, Paraguay and Argentina would be as hard to pull as the rest. Argentina spent a good part of its history in a perpetual conflict between Buenos Aires and the provinces, as in practice, Argentina could be described to work as
"Buenos Aires über alles ". The conflict only ended in 1861, with the battle of Pavón, in which the Buenos Aires forces defeated the rest of the country. Chile is not going to federate under that rules, and will need to defeat Buenos Aires to change them. There is also the fact that Chile, unlike Paraguay, Uruguay or even Bolivia, was never part of the Viceroyalty of the Rio de la Plata, so there is no prior colonial link that leads them to want union with them. Chile was a General Captaincy that once belonged to the Viceroyalty of Peru. Also, we are talking about the country that helped most in ending Peru-Bolivia, Chileans are not very integrationist. The only way to establish a federation with Argentina, instead of an Alliance, is if Chile is in charge of the Federation, if Chile is led by someone as integrationist as Simón Bolívar or if they have been integrated by force (read conquered).
The rest, true, is easier because Paraguay and Uruguay where part of the same Viceroyalty as Argentina(Remember, the largest integrationist unions OTL were formed based on the borders of the viceroyalties, as the legal justification was the Uti Possidetis Iuris). To get Uruguay to join, Artigas or Montevideo must defeat Buenos Aires, or Buenos Aires/Argentina must defeat Montevideo... and Brazil too, because they claimed it as a province. In fact, Uruguay is only independent as a Solomonic result of the war between Argentina and Brazil, which ended in a draw. To get Paraguay, Argentina must conquer it or neutralize Gaspar Rodriguez de Francia, its first independent ruler, its first dictator and an isolationist who did everything possible so that Paraguay did not join the United Provinces of the Rio de la Plata. If Francia is out of the way, support for unification can be obtained in that critical first years.
To keep Gran Colombia together, a war would be necessary to crush secessionism in Venezuela and Ecuador. Technically, it has been said that the success of federalism over centralism could also be used to achieve that goal, but in practice, it would be a union
de iure, a disunity
de facto: the result would not be guaranteed. And if I'm honest I doubt it. Just look at the history of the federations that were subsequently implemented in Colombia and Venezuela during the 19th century, or the disastrous First Venezuelan Republic. The Liberator had his reasons to doubt the "innate benefits of federalism".
Peru-Bolivia... if it becomes an indigenous based nation, then it is more likely to become
indigenista than
hispanista. In addition, Andrés de Santa Cruz had as problems the fact of having his power base in the weakest half of the Union (Bolivia), while needing to fight against the rebels
AND an intervention from Chile and Argentina. At a minimum, for Peru-Bolivia to survive, it is necessary that Chile and Argentina do not interfere, and it must be admitted that the dissolution of Peru-Bolivia benefited their national interests, especially Chile´s.
Mexico... is doomed. Too far from God, too close to the United States. Too unstable. Perhaps if Iturbide had not fighted with Congress, allowing the crisis that ended the First Empire not to occur. A surviving first empire could even prevent the separation of Central America from Mexico. Keep in mind that discounting Central America, Mexico retained most of the territory of the Viceroyalty of New Spain, but the weakness caused by political instability and successive uprisings prevented the country from defending itself well against the threat of the United States, who practically took away half of its territory.
Centroamerica... is a mess. There the conflict between conservatives and liberals, common in the rest of Latin America, degenerated into a civil war (the second since the formation of the Federal Republic) that ended up dissolving the country. There were subsequent attempts at reunification, such as the so-called "Intentona de Barrios", tried by the Guatemalan president Justo Rufino Barrios in 1885, but the opposition of the other Central American republics, as well as the United States, led every attempt to failure. Actually, I am going to leave to someone with greater knowledge of the history of Central America the task of imagining a way to save the Federal Republic.
Of course, all this corresponds to how achieve greater regional unification and integration in general, not to how achieve it through a Hispanic pan-nationalism, or how to achieve it post-1900.