A car is of no value in central Rome. It is quite compact, you can walk everywhere or take a bus or subway if the walk is too far. In the Amalfi coast the traffic is horrendous and parking extremely limited. Use the bus or the ferries to get around. Since there are 4 of you it is possible a car could be worthwhile for traveling between Rome airport to the Amalfi coast. Personally I would take the train then arrange a car to take me to the lodging.