I have been to Orvieto for 1 day, it is easy by train (1.5 hours?), and it's a lovely small town. Large unusual cathedral, picturesque town square, lots of tiny shops selling ceramics and porcelain knick knacks, small restaurants, narrow cobblestone streets. We were there for 1 overnight and that was enough time as it is very low key. Good for a nice dinner and glass of wine. Perhaps you could go for a day trip with your husband and someone else could stay with the kids that day---might be a nice place for the 2 of you for a day trip.
I do think Pompeii would be a tough journey in one day. It is 2 hours by train from the Rome station, then wait for a regional train that runs I think ever 20-30 minutes, then the train ride is about 30 minutes. That is at least a 3 hr journey, because of course you have to get to Termini 15 minutes or so before your train. When you arrive at Pompeii you have to stand in line to get your tickets, ....and if you return the same day that is 6 -7 hours in transit..that is a long day for most folks. I heartily recommend the Ostia Antica ruins which I found terrific, it's an easy 20 minute train ride from Termini then about a 8 minute, easy flat walk....the ruins are fantastic (the fish store has a tiled floor mat with the shape of a fish) and my kids could climb on things, run around, with no issues. It is not nearly as crowded as Pompeii (I encourage you to Google Pompeii (images) and see how thick the crowds are most of the time. If you are 2 feet shorter than adults, you can't see much and you certainly can't run around or climb around as easily in a crowd). At Ostia Antica, there is a small sit down snack bar, rest rooms and the ruins are fascinating. We loved it. Rick Steves has a good free audio tour. More info on Trip Advisor: https://www.tripadvisor.com/Attraction_Review-g673275-d292711-Reviews-Parco_Archeologico_di_Ostia_Antica-Ostia_Antica_Province_of_Rome_Lazio.html
If you are thinking about an apartment, I usually use Homeaway.com. We've rented 2 or 3 BR apts in a variety of European cities (including Rome) and have always had a great experience.
Lastly, Torre Largo Argentina is a centrally located, very small, site of ruins in the historic/tourist area of Rome where Julius Caesar is said to have been assassinated. (It is very close to the Pantheon). The ruins are a bit submerged (just below street level), protected by a wrought iron fence but many people--young and old---visit the area for a quick peek down onto the ruins. The real attraction for my children was watching the many cats and their antics climbing up on the rocks and ruins (The cats did the climbing not my children!). Of all the things we did in Italy, this was the #1 hit: https://www.tripadvisor.com/Attraction_Review-g187791-d246111-Reviews-Largo_di_Torre_Argentina-Rome_Lazio.html. We just returned for our 2nd trip to Rome and visited the tiny cat sanctuary where you can go in and pet cats that are being cared for at the cat shelter. We do not own cats...yet again this was the big hit of the trip. https://www.tripadvisor.com/Attraction_Review-g187791-d4416917-Reviews-Torre_Argentina_Cat_Sanctuary-Rome_Lazio.html
Have fun on your trip!
SuzieeQQ