I forgot to mention Scavi the underground tour at St. Peter's it's cool for kids but there is a minimum age. I just can't recall it. I think 12?
That tour is limited to young persons age 15 and above:
http://www.vatican.va/roman_curia/institutions_connected/uffscavi/documents/rc_ic_uffscavi_doc_gen-information_20090216_en.html
Other than the tours you can book for the Vatican Museums/St Peter's - which I would do to hit the highlights before the kids burn out on 4 miles of art/antiquities - I'd recommend skipping other tours as well. To be honest, if they can live without seeing the Sistine, I'd choose Galleria Borghese instead. The collection is excellent; the building itself is fascinating (the trompe l'oeil in nearly every room is amazing!); and the crowd control allows you really see the works without standing 5 deep. It's easily seen in the 2-hour slot that you sign up for, and will be less likely to throw the kids into overload. IMHO. If you choose to get there on foot, you'll also get to walk through the park, and the kids may enjoy that as well: good spot for a picnic, too.
Churches I would see during your three days - in addition to Basilica di San Clemente - would be:
Santa Maria Maggiore
Santa Maria del Popolo
San Giovanni Laterano
Pantheon (of course)
If you have time, take them up Aventine Hill to look through the keyhole of the Priory of Malta: the dome of St Peter's if perfectly lined up in the opening. Just down the street is very old and very interesting Santa Sabina: the orange garden next door to the church affords a nice view of the city, and is another pleasant spot for bringing a picnic.
Also of interest are the beautiful mosaics at Santa Maria in Trastevere, and (only if it won't give them nightmares) San Stefano Rotondo. The latter is an interesting, round, 5th-century structure plastered with 16th-century frescoes depicting - in lurid detail - the martyrdoms of various saints. LOL, I do not advise one this if they're very young or very sensitive!!!