The problem is disunity. That's it.
I mean, for it's first 50 years, Argentina fought to create a constitution. Why, because of disunity regarding opinions and interests.
This is my idea of a way to at least have a better Southern Cone.
San Martin somehow decides to go to Argentina by 1809. In 1810, the Junta is formed in Buenos Aires. The Junta invites representants from every Intendencia and Gobernacion and also from Chile. As they all feel that a union is safer from them(lets them all think that if Spain comes back, things gonna be hard), they form the United Provinces of South America, with this big Junta declaring independence in 1810(many people wanted to do so). Here, there will be conflict between Liberals and Conservatives, but lets have the Liberals won. They promise to get support from Europe and so many soft conservatives join them. Mariano Moreno is selected as President of the Junta Grande. His first action is to call a Congress to form a constitution. Every province sends one delegate. In 1811 its aprooved and the first major battles start in Alto Peru and Chile. The Montevideo garrison is defeated with help from every province. This means Montevideo is able to compete with Buenos Aires for commerce in a future. San Martin, Güemes and O'Higgins manage to win many battles and they start entering into Peru. At the same time, Bolivar is doing better in Gran Colombia(Spain can't react). By 1814 they have liberated all South America. After that, Spain doesn't have a base like Lima or Colombia to reconquer their colonies. So they are forced by UK to recognize the Independence of Gran Colombia, Peru and the United Provinces. The United provinces now accomplished its duty. Some want to separate but cooperation united with Moreno policies which gave many rights copied from the US, like voting for all criollo adult males(not many slaves in this part of the colonies, but Natives weren't taken in account), freeing the slaves, and many land distribution. The creation of a real army by San Martin was another factor along his figure and his determination to make this rights the rule, to keep all united. It continues to develop as an agricultural country. Cattle becomes more important for the country. Iron mining in Bolivia is very important for the first industries in Chile and the Andes. Many Natives are made to work in really though conditions and many also die or decide to emigrate to Bolivia. Another important policy was immigration. Taking the chance with Post-Napoleon immigration, the country receives many French and Spanish. With stability, its population grow well. Brazil is not a threat for the whole union(Argentina could beat them alone), and when they attempt to conquer Uruguay, it's not a close-run and Argentina manages to take Rio Grande do Sul as a new province. It's gaucho population much more common to Argentineans than to other Brazilians make it easy for them to adopt. After this, there is a military campaign which manages to take control over most of Patagonia. Malvinas stay Argentinean.
Up to WWI, progress continues, at least 3 or 4 times as many immigrants Argentina got in OTL come to the Union, with the population reaching at least 30 millions by 1914(thanks to a more rural population having more kids). After WWI, they start industrializing, they receive more immigrants, they participate in WWII, they become important, they continue doing good, etc, etc, etc.
Now its a 100 million people first world country country, like Canada with steroids.