Bear in mind that most Italians love kids - let me qualify that ADORE kids! You won't find a problem with them in any restaurant I know, and what child doesn't like pasta, pizza and ice cream, which you will find everywhere.
I can't think of any area unsuitable for children except ones you wouldn't like for yourself, i.e. too far from the centre.
I wouldn't recommend doing the Vatican with boys that age, but I'm guessing their imagination will be fired up by the Colosseum, and it would probably be worthwhile doing a tour to bring it to life for them.
The zoo (Bioparco) is great fun too, it's not huge but it's well designed, with several enclosures having those huge glass wall where you can get up close and personal with the animals.
Warn the kids about those pesky rose sellers, trinket sellers and toy sellers, who will have no compunction about placing their wares in their all too eager hands and then demand you buy them.
Rome can wear the average adult out as there is so much to see on foot, so plan your days carefully, and maybe take a hop on, hop off bus to orientate youselves with the city.
To get the most out of your trip, why not set the boys a project on the city,on the gladiators for example, before you leave? They should get a kick out of actually visiting the places they have found out about beforehand - just an idea, the most important thing is that you all have fun together.
