Just got back from a tarpon trip to Islamorada. We have been pulling the boat down and renting in the same neighborhood on Lower Matacumbe for 20 years. We jumped 26 tarpon and landed 16 this year with fairly tough weather. The neighborhood we rent in doesn't have many houses with pools. We rent there because we can pull the boat up to the back door and we are 5 minutes from the primary bridge channel we fish which works out well for a lot of night fishing.
What you will find with a lot of Keys house rentals is a lot of the neighborhoods do not allow weekly rentals, they are usually one month minimum. You may have a little better luck finding a larger condo that would offer a pool. You may also try down near Marathon in places like Key Colony Beach. I have seen several nice houses for rent there with pools.