Lucerne, Switzerland or Rome, Italy with kids

Take this with a grain of salt as coming from a non-parent, but with very close niblings.
1) I was there in late October and was wearing short sleeves (even on Mt Pilatus--this was the warmest October on record, but I would be perfectly comfortable planning an early October visit; reportedly weather usually shifts mid-October).
2) I don't know the size of Lucerne, but it felt like a small town because we stayed in the old town--I would not stay outside the old town. I can envision your family walking over the wooden bridges, visiting the castle. You can take boat trips on the lake and several mountain trips.
3) You can go to the SBB website and time all of the train rides, but the train system is as excellent as you've always heard. I think you can probably rule out Zurich with kids that young, but you might want to google each place with the terms "with kids" to see what ideas come up and help you prioritize.
I like the idea of Lucerne for a week with kids. But as an avowed Italophile (ironically have not spent time in Rome but know the lay of the land), I'd say either place would be great. Another true stereotype that is true is that Italians love children. I don't think you'd have any regrets about staying in a residential area of Rome for a week. There is enough to do that you would probably have no need to leave the city.

Regarding possible day trips from Lucerne, instead of Konstanz, I would go to Freiburg, Germany. We weren’t that impressed with Konstanz, but absolutely loved Freiburg. Also, Bellinzona is only 1.5 hours away from Lucerne. I bet the kids would like the castles.

if these are your only two choices, yes I’d go Switzerland. You can take a lot of day trips (OR NOT!) and go easily by the kids and how they are doing. You may need a day or two slow pace to start as they adjust to the time change. They may surprise you being more (or less) adventurous and with stamina. Keep it flexible, relaxed.

Rome is amazing, but so much that you’d want to see would either be lost on or not enjoyed by such small ones I’d rather save that for when they are older. We visited when our children were about 13 and 10 and that was fantastic.

Lucerne is a great place, but 8 nights there is serious overkill.

Of course, you can visit other places in Switzerland while there. We loved Interlakken and going up to the Yungfrau is good. I wouldn't go to Zurich for a day trip, but you might fly in and out of that city. Lugano is great to visit. You could consider flying into Milan, Italy and spend a day there before going to Lucerne.

Still, I love Rome for its History and Art as well as its dining.

With Kids, that age, after 15 minutes at a museum they are ready to go, so that would lean toward Switzerland.

Cost is a major factor when we travel and Switzerland, next to Norway is the most expensive country in Europe.

Rome is a bustling city- even crossing the street safely can be an adventure, with the scooters speeding by nonstop. And there's always the pickpocket issues, and your primary attention will be on your children. I'd advise delaying your Rome trip for about ten years.
Switzerland is an outdoor paradise, and the beginning of Oct is usually beautiful. The Swiss build creative and attractive playgrounds, so just Google the locations in your designated cities. I'd suggest going up to the Alps for some days, and staying in Murren or Wengen, which are delightful, slow-paced , pedestrian-only small towns. If you're flying into and out of Zurich, stay in Lucerne around those days.
Have a wonderful family trip.

Well I could. be biased but our (Swiss) railway is more reliable than the Italians......

If I was you, I'd seriously consider a town called Olten [https://dynamic-media-cdn.tripadvisor.com/media/photo-o/09/20/c4/a4/alte-holzbrucke.jpg?w=600&h=400&s=1] which is not on any tourist list. It got a nice small old town and even a covered bridge similar to Luzern. But the main thing it has going for it is that it is a major switching point on the Swiss railway system for most of the places you wish to visit as per your post - Luzern 50 mins, Zurich 30 mins , Bern 25 mins, Basel 25 mins, Lugano 2 hours 30 mins, Mt. Pilatus 2 hours, Konstanz 2 hours 30 mins and many of these are direct connections.

And because it is off the tourist trail, the accommodation prices are more reasonable.

Having just returned from Rome, I can’t imagine being there with young children. It’s so busy and hectic, and what children that age are interested in Ancient Rome, art, churches, etc.? I think it would be extremely unpleasant. I’m

Definitely go to Switzerland.

Rome with a 2-yo ? That's a 'no' for me. I'd wait 5 years or so to make sure that no nap is needed and that the youngest can at least have a basic understanding of who the ancient Romans were. A 7-year old still probably won't be very happy in the Vatican museums, but is likely to enjoy the Forum, the Colosseum, and...pizza and ice cream.

Thanks everyone! I think we are going to try Lucerne for 8 nights! We like to have one home base with kids and do day trips from there. It sounds like there are a lot of possibilities for day trips from Lucerne but it's also a quieter and more relaxing destination.

Lucerne is a great choice and there will plenty to keep you busy for 8 nights. I spend 7 nights there Sept. 2021 and 3 nights June 2022 and still haven’t seen everything I’d like to see. You can click on my name to get the links to my trip reports for those trips.

You might enjoy the growing up without borders you tube channel as they lived in Switzerland for a time and have numerous videos on the country. A lot of the Swiss cites have scavenger hunts for kids. Not sure if your kids would be too young for something like this.

This is a video of the growing up without borders kids doing the hunt in Bern:

https://www.youtube.com/watch?v=O4kcGyb0Ae4

Your kids might enjoy the lindt chocolate museum. I was there recently at the end of my Austria trip and there were lots of kids running around having a good time:

https://www.lindt-home-of-chocolate.com/en/

We spent some time last spring in Lauterbrunnen with a stop in Lucerne with our kids. We've stayed in Bavaria with them before as well. I think you'll find plenty to do in the area. We found the Swiss to be rather aloof and not as kid friendly as in Bavaria, where our children were doted upon. The cost of eating out in Switzerland is also staggering compared to neighboring countries (pricer than Kauai!), so you may want a place with a kitchen and walkable to a grocery store.

Lucerne is a great choice. We took several day trips and the one to Grindelwald prompted us to book a rental chalet for a week the next year.