S.
I can highly recommend Ann's Swimming School on SW 72nd St (Sunset) in South Miami. Both my 4 year old daughter, who was very afraid of even getting her face wet, and my 2-year old son learned to swim there. The only thing is that the classes are over for the season - the new season starts in February. The courses are 2 weeks long, you go every day for 40 minutes. Moms are not allowed in the pool, but trust me, that's better for the kids, because they can focus on learning. My son has severe separation anxiety, but by day 3 he ran over to the teachers, eager to begin his lesson. They have tons of fun. At his age, the focus is not on real swimming, but on safety issues such as them being able to float above water, finding the edge of the pool, climbing out by themselves, etc. Basically, knowing what to do if they ever end up in the water unintentionally.
Annsswimmingschool.com. I've also heard good things about Ocaquatics, but don't have any personal experience with them and don't know their schedule... I'm sure you can find them on the web as well.
S.