For background knowledge see:
George Orwell (yes the George Orwell) - Homage to Catalonia
If you are going to invoke "Homage to Catalonia", you might also mention the chapter describing the destruction of the Anarchists and Orwell barely escaping with his own life. This was accomplished by the very same Marxists the Anarchists were temporarily allied with. You might also mention that Orwell got to experience a lot of the themes from "1984" in Spain inflicted not by Franco, but by his own Socialist side.
Why do Sicilian Mafia families have gang wars? Answer, to be rid of the competition. Do they sometimes form a common front against the police? Yes.
One of the features of the Cold War was the breakup of the Communist block and the fact that Communist China and the USSR had their own little cold war (along with some hot border clashes), not to mention the split between Yugoslavia and the USSR. Robert Conquest has a wonderful quote from a Soviet general who plainly states that warfare between Communist states will be ultimately bitter and eternal.
And sometimes they pulled together against the United States and the Western world.
As an aside, you also might want to explain why any sane person would be better off ruled by the Spanish Republicans (read Socialists run by Communists) than by Franco. After all one of the triggering incidents was La Pasionara (Communist spokeswoman) proclaiming that the parliamentary leader of the center-right party was a dead man and then him ending up dead, killed by Republican Guards.