In 1865, Spain attempted to annex the peruvian Chincha Islands, Chile, Ecuador and Bolivia allied with Peru to prevent the spanish from annexing the islands, Brazil prestige was raising after the Christie Question; many latin american navies started to use ironclads and monitors during these decades; even during 1885 chilean navy alone was powerful enough to stop the american fleet, not counting with the combined strenght from the other latin american fleets; during c. XIX the wounds from the independence wars were still open so if another nation tried to invade and control various latin american natios, this will easily trigger a second war of independence and this time more organized and with more international support; speaking of that, the British Empire is very interested in South America and they wouldn't like to lose their influence over there...
The answer is no, the United States can't control all of Latin America, even conquering Mexico would be expensive and I highly doubt that the americans would allow that