EU drivers license and car insurance

I would get an international drivers license. Readily available at the auto club. Get one for each driver and bring with your American license.

As far as insurance, I get the full coverage at the rental agency. I'm sure it might be more expensive, but I don't want to worry what my auto policy covers out of the country, or problems with the local rental companies. Just makes it easier to deal with. Peace of mind and enjoy the journey.

It all depends on which country issued your current licence. You don't say where you are from, which is always useful information when asking such questions.
You cannot get an Italian licence without passing a driving test in Italy. But you don't need an Italian licence.

If your current licence is from an EU/Schengen country, it is already in the EU format, can be read by Italian police and is valid.
If your licence is from a non-European country, then you need an International Driving Permit. This is a legal document which both (a) certifies your licence as valid, and (b) translates it. You must carry this along with your original licence, neither is valid without the other. You must get the IDP in the country your licence is from. You get it from an organisation authorised by the government of that country, usually the local automobile club. As I don't know which country you are from I can't be more precise.

Sicily is part of Italy, the same rules apply.

Just to clarify, there's no such thing as an "International Driver's License". What you'll need to get is an International Driver's Permit, which is used in conjunction with your home D.L. (it's compulsory for driving in Italy). These are easily available for a small fee at any AAA/CAA office for a small fee, and are valid for one year.

When renting cars in Italy, a part of the insurance must be purchased from the rental firm. You may find it helpful to download the car rental information booklet at gemut.com....

http://www.gemut.com/car-rentals/free-rental-car-booklet.html

In addition to the license considerations, you'll also have to be aware that there are some potentially expensive "caveats" when driving in Italy. You'll need to be extremely vigilant to avoid the dreaded ZTL (limited traffic areas) which exist in many towns and cities. EACH pass through one will result in expensive tickets, which you may not know about until several months after you return home. There are also automated speed cameras (including the devious Traffic Tutor system (which measures both instantaneous speed as well as average speed between two points - violate both and expensive tickets will follow), parking charges and tolls. You may find this recent forum thread to be interesting......

https://community.ricksteves.com/travel-forum/italy/car-rental-traffic-violations

I meant the International Driving Permit! Sorry for the confusion.

I suppose this is obvious, but Sicily and Italy are the same. It is like saying Florida/US.

I believe the permit is required for Italy -- we did have to show ours when we picked up our car (but we were told it wasn't required for France and no one asked for it). We got ours at our local AAA office and it was pretty fast/easy. I could not waive the Collision Damage insurance as part of my rental costs in Italy, so you'll be covered for some aspects of it anyway.

It - or a certified translation - is required in France. Maybe not by the car rental dude who just wants your money and to pass you the car, but if you were in an incident or stopped by the Police they certainly would be interested in it.