Remember that Francisco Ramírez fought against Brazil in the Platine War, and was actively fighting for freeing the Banda Oriental from Brazil. He would not accede to become a client state or any kind of support from Brazil.
The Republic of Entre Rios was not really an independentist state, but rather a rebellion against centralization of power in Buenos Aires. It even attempted to make Paraguay rejoin the Argentine Confederation and help him defeat the Brazilians in the Banda Oriental; when he was refused he actually tried to invade Paraguay. If Entre Rios was invaded, I think there would be an effort by Buenos Aires and the rest of the provinces to repel the Brazilians, much like the Platine war. It all depends on who's on charge, and I'm a little rusty on my civil wars history at the moment. After Ramírez and the end of the Republic, Entre Ríos still acted, like most of Argentina's provinces at the time, as an independent state loosely bound by interprovincial treaties.
Any change at this time could result in a completely different Argentine Civil War(s). The unification of the nation might happen sooner having Brazil as a common enemy. I doubt Brazilians could advance beyond the Paraná, and I think Paraguay would have been involved, seeing as, while they were plotting an independent course, Brazil would be an inmediate threat to both Argentina and Paraguay.
Would having the ports of Montevideo and Posadas not be a gamechanger for Brazil? I'd think it'd allow earlier economic exploitation of the interior of the country and greater access to global trade.
Posadas was an undeveloped town, and to reach it from the river is nearly impossible because of the Iguazú falls. Montevideo is a good port and has much potential, but Brazil isn't lacking on Altantic ports. In fact the city might have less development due to hostile relations with its traditional parterns in the Rio de La Plata. It could become a major regional capital though.
About the only major butterflies I can envision would be altering the Paraguayan war, or stirring up a war between Argentina and Brazil. The POD doesn't really change the power structure of the region, or progression of events in any of the countries (except, obviously, one tiny country created and one tiny country extinguished). Losing Entre Rios/Corrientes/Missiones doesn't have any significant consequences for Argentina in the same vein as losing Silesia did for Austria, and gaining/keeping Uruguay doesn't have any for Brazil same way gaining/keeping Silesia did for Prussia. People (such as Urquiza) and hence events will change and this may possibly have huge consequences, but nothing obviously predictable.
Nothing Ever Happens In South America, amirite? Because those European countries actually have events that
matter, unlike in South America where they just
don't because of reasons.