I live on Big Pine Key about 15 miles from Bluewater RV Park.
The Key West NWS office is great and keeps their Facebook and websites current regarding local weather.
On my iphone, I use the Weather Underground app and their separate app called Storm. As rain in the Keys tends to be localized, the Storm app shows the predicted path of each storm cell so you can determine if the rain is going to hit you or pass you by.
As you're driving down, you should also use Google Maps which will show you live traffic. There's some construction near the end of the FL Turnpike that causes some backups. Also if the 18 mile stretch of the Overseas Highway between FL City and Largo backs up, it will route you around to Card Sound. Once you're past Largo, there's only one road so you just have to bear with any traffic. Fortunately, traffic tends to be light in September and October.
The weather has actually been pretty good the last few days. Some rain but definitely opportunities to go outside. It's been hot and humid though!
If you need any more local info, shoot me a PM.