The current predicted path at https://www.windy.com/?2017-09-11-09,28.442,-80.717,8 looks like it will be going right up the middle of the state just like your image shows. If it pans out like this, my family is right in the path. :(
I would tell your family to pay close attention and be ready to go if there is any chance they are in real danger. There are several models now showing a trend to the west. Even the NHC is moving it a bit west. But who knows. Everything could shift east again.