September is not a good time to go. As others have said, it will be hot and humid.

The following backs up the common belief that September is a bad time for hurricanes:

hile the Atlantic hurricane season is "officially" from 1 June to
30 November, the Atlantic basin shows a very peaked season with 78% of the tropical storm days, 87% of the minor hurricane days, and 96% of the intense hurricane days occuring in August through
October (Landsea 1993). Peak activity is in early to mid September. Once in a few years there may be a tropical cyclone occurring "out of season" - primarily in May or December.

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Did you catch that 'Peak activity is in early to mid September.'?

Hurricanes can affect an area hundreds of miles in extent, with heavy rains, flooding and even tornados.   

I live 700 miles from the Gulf of Mexico, yet when a big hurricane strikes, we get rain.

I believe your kids need to do some more research before dedicating time and money to this trip.