Welcome to CMP!
I'd avoid August which will be the most crowded month as anywhere around the Mediterranean Sea and even more so in Italy. Also, the heat down in Sicily during the day could be difficult to take for (small) children.
Other than that, I do believe regarding water temperature, there's not that much difference between July-September. However, I'd rather go early in September, also because days are still longer then and you'll get more daylight.
I'd choose September (prices then might be lower as well).
But you choose!
For temperatures (air and water), I just googled and found a site you may want to have a look at:http://www.sicily-vacation-home.net/sicilyinformation/weather/index_eng.html