I think that an even more relevant example than the process that led to the British takeover of the Dutch Cape Colony is the process that led to the British takeover of Quebec starting in 1759. In that situation, in Quebec City, French soldiers were ferociously against a British takeover (similar to how ferociously against the British the local militias in Buenos Aires were in 1807), but they lost anyway at the Plains of Abraham in 1759. And the French fought back in Quebec City in 1760 and won, but by that time it was too late anyhow for the French. So too, the Buenos Aires and other Rio de la Plata creole militias would doubtless have attempted to fight back after a decisive British victory, but it would have been too late for them.
Regarding Britain and Spain as allies from 1808, the British invasions of Buenos Aires took place before the 1808 takeover of Spain by Napoleon; it was that Napoleonic invasion that led the Spanish colonies to recognize the previous Spanish government as the legitimate one. In other words, Spain had been on France's side for a short while before 1808 (which is why the Brits invaded the Rio de la Plata in the first place), but now the Spanish in Latin America were on the same side as the Brits. As Colonel Troutstrangler has indicated, the Spanish Empire (which was seriously weakened at that point) was in no position to demand anything and indeed asked for British assistance. So, the Brits definitively keep the Rio de la Plata region itself and give back (for the time being, as a friendly gesture) most of the interior (which was, just like the Rio de la Plata, in the Viceroyalty of the Rio de la Plata). This is where things get interesting....
I think that with regard to the interior, sure, the Spanish and creole forces will make it difficult for the British, but the British gradually make inroads there anyway. To me, it's no real different from the situation in the Boer republics of Natalia and interior South Africa in the mid-late 19th century. At first, the British will prop up and support independent Spanish-speaking republics (as a buffer for the now-British-held Rio de la Plata). Later on, as more British settlers come first to the Cordoba area and later to the Cuyo and Tucuman/Santiago del Estero regions (the way British settlers pour into Natal, the Transvaal, and the Orange Free State in South Africa), these areas eventually get formally annexed into the British Empire just as those areas in South Africa got annexed to the British. Just as gold and diamonds brought British settlers to the South African interior, so wine in the Cuyo, sugar in Tucuman, etc. bring in new British farmer settlers. (Salta/Jujuy becomes a part of Bolivia because of the different military dynamics of a British Argentina vs. OTL Argentina.)