The movie was "Popi" with Alan Arkin and Rita Moreno and even iMDB is barely aware it exists.
I think it was the best Hollywood satire of that period (and nearly as good as my favorite film of all, "White Voices," which was Italian and is even more forgotten, although it was prominent enough to be reviewed by Time -- "one long leer," said the reviewer who was a dense as most Time reviewers).
- Abraham is a Puerto Rican single parent with two boys. He is becoming very worried about them living in their run down neighborhood when one day he notices that Cubans who escape are lionized and given exceptional benefits. He thinks up a plot to have his sons washed ashore as cuban immigrants who will be adopted by rich anglos.- Written by John Vogel <email@example.com>
Besides the content, I liked "Popi" because the satire was somewhat restrained, unlike most of the satires of that period like "Dr. Stangelove" and "The Day the Fish Came Out."
When the Cuban fascists moan, think about the lesson of "Popi."
And the other lesson, which you do not get from the movie but is very obvious -- America has always been more welcoming to fascists than to democrats.