I think that we had a successful trip to Rome and saw everything that we could reasonably expect to see during a 4.5 day visit with three kids. If we exclude the luggage arriving 30 hours after we did and Muriel vomiting in the taxi on the way to the airport, I would say we had a very good trip.
Our apartment was located at Via dei Coronari 222, which was within walking distance of most sights. The Colosseum was a bit of a walk for Niamh, especially in the rain, but she managed to do it. It might have helped that she knew there would be gelato at some point.
Our double stroller was about 5 cm too wide to go on the busses without disassembling, so we used taxis every day. Using a taxi was less expensive than I had expected and saved us quite a bit of time. It was nice having a taxi stand about 100 meters from the apartment. We didn't use any car seats, so I was a bit nervous about getting into an accident. That being said, the driving was not nearly as scary as I had expected it to be. There was only one time when I thought we would hit somebody and that was the pedestrian's fault.
If you have been following us in Facebook, you will know that we ate our (or maybe more than our) share of gelato. Here are a few of the places we wanted to visit. I'm not sure how many we actually sampled.