I genuinely have little difficulty with getting through Miami, particularly if terminating there (as the poster says they will) rather than connecting, which is where the Iberia and other problems seem to have focused on). Yes Miami's non-English speaking community that work at the airport can be annoying, but it's overall a pleasant city.
Stay in a hotel on Miami Beach oceanfront rather at the airport/than in the city. It's a 25-minute cab ride.
Everglades are great. Rent a car, get a good map, and drive down through them.