Getting a Rental Car in Rome

Use a consolidator such as:
www.kemwel.com
www.autoeurope.com
Select the "no insurance excess" (no deductible) option for peace of mind. Neither your US insurance nor your credit card is likely to cover you in Italy.
The above consolidators are actually the same company now (they merged years ago). They are based in Maine and work with the major rental companies in Italy (Europcar, Hertz, Avis, Budget, etc.). Once you go on the sites check the prices and select the best option for your need.
To get out of Rome's traffic more easily, select a pick up location at or near the Tiburtina station. From there it's an easy hop on the Tangenziale Est/ A24 freeway to Abruzzo.
Offices generally open from 8am to 8pm. Only the airports locations stay open beyond those hours. As such you may have to keep the car overnight, or leave early in the morning so that you can be back by closure time. Otherwise you need to travel a bit further and return the car at the airport (no extra charge for returning at a different location).
From Rome to Tussio is a good 2+ hour drive. Since you are not familiar with the area or driving in Italy, give yourself 3 hours also for the rental car paperwork. If you rent early in the morning shortly after opening hours, you should be at Tussio by noon. Knowing how Italians are, once you meet your family, it's unlikely they'll let you get away with just a few hours' visit and leave. Chances are you'll be stuck there for a huge lunch, plus visiting all your extended family. It might be days before you can free yourself from your Italian family and escape home. If you plan to visit Rome at all, I recommend you do so before you visit your family, because once you see them they won't let you get away and you will have to escape in the middle of the night while your Italian family is sleeping. You may want to plan to spend a few days there instead of just a few hours.

Thank you for the information - it really helps!

Do we need to get any sort of documentation to be able to drive in a different country? Or will our passport be sufficient?

You need the following documents:
- your passport
- your driver's license issued by your home country/state
- the International Driver Permit, which can be obtained at any AAA office in about 10 minutes with two passport photos and $15.

Thank you Roberto!!