Deep in the hazardous and ecologically fragile Everglades, hundreds of migrants are confined in cages in a makeshift tent detention facility Florida’s Republican governor calls “safe and secure” and Democratic lawmakers call “inhumane.

Days without a shower or prescription medicine.

The ensuing battle over the jetport, which eventually drew in then-President Richard Nixon’s administration, was the catalyst for creating Big Cypress National Preserve, and helped shape the environm...