What planting zone are you in? Here in OKC I'm in Zone 7, so I think we get a little colder and maybe a touch more moisture, but in the main it sounds like your issues are our issues! Extreme all the way: heat, ice, drought, an occasional flood, etc. Do you want a tropical look or do you want something more traditional? We made a list on another forum for good poolside plants (#1 rule - minimal shedding! Unless you just love to skim Crud out of your pool, then I recommend you plant a crape myrtle right next to it like ours and you'll get all the skimming you want!) which I think were heavy on the hardy tropicals, let me find it.
Also, when you say privacy near the fence, which is more important - density or height? Or both? I think height is for visual privacy (we have two story houses surrounding the pool) but density is more for sound privacy (like you don't want to hear the neighbor's conversation when they are in their pool, or their barking dog, or whatever).