Depending on where you want to go, I wouldn´t go any later than March (if you plan on traveling south). Once in April I had terrible fog @ EZE and we were diverted to COR for a couple of hours. But then, people don´t go to EZE for the weather. The most civilized airport gateway is SCL, by quite a distance. Rio can be still quite hot in March.

I think that if you want to do A,B,C, you do them in the order C,A,B. I´d start in Chile, go south for some very nice sightseeing, then fly to EZE, and then end in GIG. GIG/SCL is quite a distance and you won´t want to connect back through SCL to get home. EZE/SCL aren´t that far apart, and I have made that connection many times.

Note that Sarah Palin photos you may have on any electronic device will be confiscated and treated as the worst form of pornography down here, so don´t say you weren´t warned

In case you are wondering how stale my advice is, I am at the Lan lounge @SCL, awaiting my flight to EZE after spending 3 lovely summer days here in Santiago