I'm thinking, at this point, due to time, we'll probably have to cut the visits to Dover and possibly Stonehenge and Highclere.
We live in a rural area, so 90 miles away is 90 mins, so I forget how much transit time to allow.

We may well end up cutting MSM and Normandy.
Regarding MSM, here's what's tricky. My wife just mentioned as a place she's always wanted to go to, so I was trying to do everything I could to fit it in, but I don't know that she knew when she mentioned it how messy it makes things...and once I bring her up to speed on what a mess I've caused on these boards, she may say, "Wisconsin Dells it is!!"

You might consider visiting the Eiffel Tower at night. It is usually less crowded then and the lights glow and "twinkle" every hour on the hour for about 5 minutes. I am not sure when your trip it taking place so just double check to make sure it the tower is open during the evening when you will be there. Also, this is another good place to get tickets in advance.

I think Venice is a must just b/c we've grown up seeing it in movies, TV, and it was on the top of their list, even if for only a couple of nights.

If we WERE to trim Venice and add on Pompeii/Amalfi Coast, is a couple of days good enough (yes, I know 3 weeks is ideal), but would be be better just extending Rome to simplify?

As I look more, we may just opt to extend in Rome to avoid constant moving around.

If you end up going to Bath, I think the Bizarre Bath comedy walk is a must for families. We had so much fun on the walk and still talk about it many years later: www.biararrebath.co.uk. We also rented a small rowboat and enjoyed a few hours on the river. You will want to visit the Roman Baths as well. We visited at twilight which was a nice time as the baths were beautifully lit.

I agree with a poster above that the Tower of London is a must. I would save Dover for another trip. I haven't been to Highclere so can't comment on that.

Also, London theatre can be terrific. I would try to check and see what plays might appeal.

I must admit, I don't know understand you are seeing a MLB game in England. That will take up a lot of your valuable time.

Ok - looking more at Pompeii and I think my kids would be fascinated. So, although it's long, 2.5 hours by private car wouldn't be horrible from Rome.

We are diehard fans of the Chicago Cubs and they are playing a 2-game series against their arch rivals, the St Louis Cardinals at the end of June. We're not coming to London FOR that, but since we can shuffle our dates to make sure and see a game (or try to get tickets), we cannot miss the opportunity.

Your kids would probably like Venice the most of all the places you have mentioned. Don�t cut it from your trip!

Your reasoning for listing cities separately for comments, thinking people who have traveled to only one could give advice without scanning long threads is completely understandable.
However, I believe (not proven by statistics, but by being on this site for so long) many posters here have traveled a lot and many live in Europe, so they are familiar with all of your bases and with the logistics of getting from place to place and country to country. These most knowledgeable posters now have to look at multiple threads to keep up with your plans and to give advice. When things have changed, they are still commenting on old itineraries. That is why it is easier to get all “ducks in the same lake” to keep them in a row, so to speak. It is so much easier to help if one itinerary is posted, with all cities, countries, etc. As things change, those changes will be in the last, unread posts. Nobody has to go back and re-read things. There will not be duplicate comments in multiple threads.
Please, believe me, this is really meant to be helpful. It will make things far less confusing and “messy” as you say.

For now, people have to go back and forth from Paris and London to comment on your ideas/plans for Italy.

I am just going to go ahead here. Looks as if you are now considering to skip Venice and head south to see Pompeii or spend more time in Rome. Most kids love Venice. I can recommend some guide books for Kids for Venice if you decide to keep it. Also, taking a vaporetto out to the islands like Burano, is wonderful. Going up in one of the bell towers is fun. If you go, will make further recommendations. Venice can be suffocatingly crowded, as can many places. Once you decide, people can advise on how to mitigate that.

Pompeii is very interesting, but with kids, I strongly do not recommend it as a day trip from Rome! Ostia Antica is near Rome and is an interesting, easy archeological site. If you are going to see Pompeii, please spend a night or two in the area and do it from Naples or Sorrento. If you do go to that area, there is a tour of the underground excavations of Naples that might be fun for the kids. You would also want to go to the museum in Naples that has many of the artifacts from Pompeii. That “brings to life” a lot of what happened in Pompeii.

Since you are dropping Greece and Switzerland, you have four weeks. Consider simply saying, we will do
1. Paris and environs: 7 nights (6 days), (3 in Paris, 1 for Disney, 2 for MSM)
2. London and environs: 8 nights (7 days)
3. Italy 12 nights (11 full days): (Venice 3 full days, Rome 4 full days, Naples - Pompeii - AC 3 full days).

This leaves some travel days. This is only a suggestion on how to simplify, alter to suit your preferences. You have listed only one city each in England and France, so easier to mesh things together. Italy requires much more travel time and logistics, especially if you are doing two or three places not really close together.
If you decide to include Venice or Naples, try to make one of those your departure or entry city, not Rome, so you do not have to backtrack.

We get sentiment that all the time -- but do you really?? Locals mostly eat at home and maybe go out to a restaurant or wine bar or pub a couple of times a month. Otherwise they are working remotely or in the office, doing laundry, the school run, shopping at Waitrose or Sainsbury. Pretty mundane just like anywhere else. Most visitors honestly don't want to live the locals day-to-day lives. They want to see the famous parts of Paris or London

With such a short time, I'd skip Naples and Pompeii and just enjoy Venice and Rome. Going to Naples and seeing Pompeii is like going to Disneyland and just being able to go on one ride. You should dedicate more time to the Naples area to do it justice.

There's so much to do in both Rome and Venice but one always must account for travel time.

Venice: Definitely go to Burano and spend at least a 1/2 day there. It's a different world full of quiet areas and colourful houses.
Rome: Stay in Trastevere, book a morning bike tour of the city, see the Coliseum, the Vatican and do the walk between Navona and the Spanish steps. Explore Trastevere in the evening, and if you have time, choose another area to explore. That will fill your 3 days easily.

Sassafrass' break down for days/nights is a good starting point . . . but IMO/IME you'd need considerably more than seven days for London/environs since you have mentioned the baseball game, Harry Potter sites (including both the WB studio tour and Oxford), Dover Castle and the Cotswolds, plus iffy/'maybe' destinations like Bath, Stonehenge and Highclere. A family would want a minimum of 5 full days/6 nights IN London to barely scratch the surface. And a day or two more if visiting Hampton Court and/or Greenwich. Plus Oxford, Dover, and anything else

If driving from Paris to Normandy you can visit Giverny on the way.

https://flic.kr/p/8kUAyY

To confirm: Trastevere would be a good home base/central location in which to stay?

KTtravel -- if you need it explained you'll never understand Anyone who's a diehard fan of any major team (whether the Cubs, Celtics, Niners, Packers, Real Madrid, ManU, whatever) will totally get it.

Preach!

A great thing about this site is that everyone has their favorites and you can glean something from all of us.
Italy with kids is always different, since most can handle just so much art (but they will have a greater appreciation for it once they've been).
My preference is always to do Italy by itself. No need to combine with other countries since it has so much to offer and requires a day of travel to get there from Western Europe/the U.K.

But sticking with your original city choices, I'd start in Venice, take a private water taxi into the city (IMO, more memorable than the gondola, but which you have to do on your 1st visit)
Stay somewhere in Venice proper, not on the mainland, since the night experience is so much better after the day trippers have left. Gondola doesn't need a reservation & flat fee for your whole family
Doge's Palace, glass demo somewhere (don't need to go to Murano to see it), & just wander the streets.
IMO, the 1/2 day you arrive, a full day, plus another morning is enough to get a good Venice experience.

Find a cheaper way to the train station and take the afternoon express train to Rome. The bullet train ride alone is an experience the kids will like.

Rome: Got hit the big sites! Vatican/Coliseum are best with a pre-booked tour. IMO, the Vatican is best as the first tour of the day, or late afternoon.
Coliseum tour that includes the underground or at least the Arena floor. Stay centrally & you can walk to most of the famous sites (Trevi/Spanish Steps/Pantheon)
We really loved our Appian Way tour as well.

I really like using the GetYourGuide app and booking all tours thru them. Consolidated ticketing and friendlier cancel/change policy than booking yourself.

We have merged your three threads and modified the title to include all four cities

Any suggestions on what specific neighborhoods to search in?