Travel route suggestions Paris-Amsterdam-London

I would go for flying into either Amsterdam or London, then taking the train to Paris ending in the other city.

There are tour to Bath from London that include other places like Stonehenge.

Haven't been to the Eiffel Tower in some years.

Here is an expensive skip the line tour.
https://www.viator.com/Paris-attractions/Eiffel-Tower-tours-tickets/d479-a89?pref=204

Here is the official ET site where you can purchase tickets
http://www.toureiffel.paris/en/preparing-your-visit/buying-your-tickets.html

All three cities can be done without taking a tour. Amsterdam is very walkable and you might want to take a canal tour. London and Paris have great subway systems. You can do them on your own with a good guidebook.

Amsterdam-Paris is the Thalys train service; Paris-London the Eurostar. The reliable www.seat61.com/ informs you about the practicalities, including the discounts with advance reservation on these trains.

I would start in Amsterdam in preference to London. A short Belgium stop en route between the two would be an option to consider as over time in Bath ... Amsterdam (3) > Belgium (2) > Paris (5) > London (4)

Fly open jaw to avoid back tracking. Investigate which options work best for you on your given dates.

The best option between London and Paris or vice versa is the Eurostar rather than flying. Tickets are available c 6 months out for the best prices. Friday night, Sunday night and Monday morning tend to be the busiest and therefore more expensive times to travel.

Amsterdam to Paris is either the train or fly. Amsterdam to London - the quickest option is to fly. Also consider flying from London City Airport in addition to the usual airports.

Bath is easily doable by train from London as a day trip, but IMO there are other places that children would prefer to visit that involve less travelling. Most seem to like Harry Potter World plus Greenwich! Windsor or Rye make good day trips.

Bath is nice but would take a whole day out of your London time. With two weeks for three great cities I'd stick to those cities. Maybe a day trip to Windsor or Versailles or some such, but Bath involves too much travel time for what you get in a short day.

Good train connections among the cities, Thalys and Eurostar. Go Amsterdam-Paris-London or the reverse.

I think your itinerary is very reasonable. You can get tickets to key sites early, keep checking, some have a limit like 6 months out some more. I would reserve sites for first thing in the morning, that way, you wake up have breakfast and head straight to the site. Then you have the rest of the day to hit the rest of your sites.

I would start in either London or Amsterdam and track either way.

Amsterdam 3 N,
Brugge, 2 N, 2.5 hours to Paris, called Venice of the North. A walk along Minnewater lake is a nice way to enter town. Take a canal tour. Zevendel Hemmel is a great place to eat. I have been visiting here for 23 years. https://www.tripadvisor.com/Restaurant_Review-g188671-d1045501-Reviews-De_Zevende_Hemel-Bruges_West_Flanders_Province.html
Paris, 5 N, a visit to Versailles or a castle tour of the Loire valley is nice. Castles and palaces are a change of pace from the big city.

London, 4 N. I am not sure about Bath. I have been, but it has been a while, 23 years.

I would get out of London and Paris for a day to see the smaller cities and country side.

I have a 10 year old. We get her into the trip planning and try to see something she thinks is interesting. We like to find something for her everyday, a small park to play or a gelato shop or chocolate shop. Get your kids to read books about the destinations. I have heard, Lonely Planet and others may guide books for large cities like London and Paris. When we go overseas, we start learning a foreign language so our 10 year old can order off the menu. We have done it in Italy and Germany. Once she learns a word, it is only spoken in that language. Even if you learn one word a week, you can memorize about 20 words for the trip.

Enjoy.