Becky, I haven't taken this tour but HAVE walked a long stretch of the Appia (athough skipped the Aqueducts) so will take a stab at this as no one else has responded yet. :O)
First off, here's a youtube someone posted of their Appia TopBike Tour this past May that you might find useful? It'll give you an idea of the sort of surfaces and conditions you'll be riding on/in. It appears to be the 6-hour tour as they stop at San Sebastiano catacombs (or it may be San Callisto depending on which is open or not on the day of the tour) and for the wine/cheese break that aren't included in the 4-hour tour. Otherwise, the website states that the itinerary is exactly the same.
https://www.youtube.com/watch?v=BijzwCnvRik
You'll note that there are stops along the way for the guide to provide information on some of the landmarks, and that you'll just be riding by others. Unless you're doing it on a Sunday - when it's closed to vehicles - you will have some traffic here and there to contend with although the guides appear to do a good job of helping the group safely across busy intersections.
They very carefully word the itinerary as "while going past an ancient sepulchre, a Roman statue, the ruins of a circus and an imperial palace" and "going through the Caffarella Park" so no, it doesn't look like you'll be visiting the interiors of anything along the way. Even on the longer tour, the only interior they specifically mention is at one of the catacombs.
We did San Sebastiano on our walk and thought it was interesting but would have enjoyed the day just as much without it. The scenery was the star, and it was wonderful to explore countryside so close to the city! You'll pedal by or stop for a look at all sorts of ancient ruins and relics, and we found the crumbling remains of the many tombs which once lined the Regina Viarum to be fascinating. So, I don't know as you can go wrong with either tour. Given the summer heat and age of your youngest, I might be inclined to do the shorter morning/early afternoon tour which, at € 55,00, is very reasonable, IMHO, for 4 hours with a guide and equipment. BTW, the electric-assist bikes are seeing high praise from reviewers of the tours on TA.
Hope this helps?