London, Paris and Normandy itinerary suggestions?

There are World War II tours offered by London Walks. They’re two hour walking tours, just show up and pay £ 10 each. They also have tours covering almost everything. https://www.walks.com/walks-by-day/sunday/#westminster-at-war

There’s a sister company in Paris that offers the same thing.

The Dday sites are kind of spread along the coast with no easy drive between. More of a zigzag along country lanes. Be sure to do lots of research on the sites you want to see.

Bayeux for three nights would be nice and, IMO, no car needed. Take a guided tour — full day — of the D-Day sites. We did this tour https://www.normandy-sightseeing-tours.com/d-day-tours/full-day/tour-e-1-u-s-beaches.html and felt we got a great overview and saw lots of countryside. The guide was French and that lent a locals perspective. Not cheap, but you will get so much more out of a tour than driving yourself and trying to figure out what you are seeing and what happened.

The other day there you can see the sites in Bayeux and go over to Arromanches, which should not be missed. You can taxi or take a bus to Arromanches. The museum and sight of the harbor that was created to support D-Day were mind-boggling to us as we had not stumbied across any of this info in our education. The Bayeux Tapestry did not really interest me until I saw it! Time well-spent.

Absolutely do a DDay tour--it was the best money I ever spent. If you try to drive yourself to the sites, you'll just see beaches and a church and have absolutely no idea of what happened there. A good guide will bring it all alive. Rick Steves lists some in his France book, and you can also look in Tripadvisor.com . We used Alan Bryson of www.firstnormandybattlefieldtours.com and he was great.

His review is here https://www.tripadvisor.com/Attraction_Review-g187181-d2661109-Reviews-First_Normandy_Battlefield_Tours-Bayeux_Calvados_Basse_Normandie_Normandy.html

Also your kids should enjoy the catacombs and the Sewer Tour in Paris. Google them

Another vote for a full-day beaches guided tour. It's not about transport; all about the guide and the context and perspectives he/she will provide. Routes will vary depending on whether the tour is oriented to the US or Commonwealth beaches. Most run from Bayeux but Caen is an alternative base. Being larger, it offers more alternatives for hotels, dining, car rentals, the peace museum and its own history as a centre of the subsequent tank battles. William the Conqueror's fortress castle is also worth a look.

I hope you are using a multi-destination search function to fly into London and home from wherever your cruise ends.

https://en.voyages-sncf.com/en/ will show the train route from Paris to Normandy. You probably cannot get a train that will reach Normandy early enough to take a full tour the same day.

Don't miss the amazing 900 year old Bayeux Tapestry telling the story of the Norman conquest of England.

It is difficult to take full advantage of multiple days in Bayeux without a car. But paying the high prices for escorted D-Day tours with transportation is a common solution. Of course, tourists willing to do the research work can have a busy and fulfilling day or two of touring (with a rental car) entirely on their own. Even our host Rick covers a lot of detail in his France books.

Other travelers like to have a guide, and skip all the planning work. I personally didn't care for the gung-ho demeanor of the Normandy beach guides I heard all around us. But they deliver value for their fees, no doubt about it.

I liked the Peace Museum in Caen, but it covers a broader span of time than most--from the lead-up period to the car through the Cold War. It's roughly a full-day commitment if you want to see the whole thing. The Museum of the Battle of Normandy in Bayeux (a bit of a walk from the center) is modern and more focused and can probably be seen in less than a half-day--though I don't remember exactly how long I spent there.

I am yet another who urges you to take a D-Day tour rather than trying the do-it-yourself approach, assuming no one in your group is a D-Day scholar.

The relatively new Civilians at War Memorial in Falaise (car needed unless you want to bus there from Caen) is very interesting. It's a museum, not a monument, and nearly 100% English-accessible. It includes coverage of Resistance activities. I think you'll have plenty of D-Day/WW II sites on your itinerary without it, but it's in the area and I wanted to mention it to you. I'm not sure how long I spent there--probably between 2 and 4 hours.

A complete visit to the Churchill War Rooms is at least a half-day affair and could easily take close to a full day, because the Churchill Museum segment is comprehensive and time-consuming. If you just want to pop in to see the rooms where things happened, that will take less time, but you may not be thrilled with how much you paid for that privilege. You should pre-purchase tickets for the CWR; the ticket line is very long and tickets can sell out.

The Imperial War Museum takes a lot of time to see--definitely more than one full day if you want to see all the exhibitions (some permanent, some temporary) and read all the explanatory material. The posted explanations for the main exhibition are heavily duplicated by the audio guide, so each visitor can choose one or the other. I recommend taking a look at the museum website before your trip and deciding what parts of the museum you're prepared to skip. If you try to make a comprehensive visit to the whole thing (including the detailed exhibition on the Holocaust and to the Churchill War Rooms, there will be time for little else in London.

I agree that the London Walks are very good. The cost is £10 for adults and £8 for children. I'm not sure of the age cut-off.

One full day in Barcelona is way, way too short for that city, which has at least ten highly popular attractions (most related to Gaudi) that require pre-purchased, usually timed tickets. That situation makes a blitz visit very challenging. Four nights is a more reasonable minimum, given all there is to see in the city, and that will still be rushed.

The Bletchley codebreakers museum is an easy train ride from London and touches on issues besides the secret war since the innovations there are considered a lead-up to modern computing.
https://bletchleypark.org.uk/

We wound up doing Paris and Normandy on two separate trips because there is so much we wanted to see at both locations. For Normandy we spend five nights in Bayeux, taking Dale Booth's 2-day American Beaches tour (so worth it, but he books up well in advance), taking a day to see the tapestry and the cathedral, and a day of renting a car and visiting Honfleur (which you could skip). We stayed at the Hotel Reine Mathilde in Bayeux back in 2013.

If you haven't already, encourage your teens to become involved in the planning process. I view it as a life skill, like tying shoelaces and learning to cook and mend. "Must sees" vary by the interests of the people involved, so encourage everyone to do some internet or guidebook research and bring their list to a family meeting. Then the negotiations begin, but try to get something for everyone. My day at the Grand National (a famous horse race) turned into an afternoon at Lingfield Park (think local track) but I had a great time.

We have been to Normandy twice and have always rented a car after taking the train from Paris to Caen. I can't imagine touring the area without a car due to its size.Be aware that car rental agencies are closed on Sunday and also check the hours they close for lunch. As previously mentioned, a tour is money well spent as a guide will provide you with information necessary to really understand and appreciate the sites. On our first trip, we booked a private tour with Sylvain Kast and it was worth every cent. He gave us a great overview of the area, which enabled us to spend the next few days exploring on our own. We have a family member who served in Normandy, and Sylvain conducted research on that service before our arrival. Highly recommend!
https://www.d-day-experience-tours.com/tours/ While in Normandy, we based ourselves in Bayeaux which was extremely convenient.