Reccommended days for Amsterdam, Brussels/Bruges, London, and Paris

My suggestion, I would cut out Brussels and spend the time in Bruges if that is a must see and it is very nice city. I also think you need to consider the time it takes to check in and out of hotels get to train stations, board trains, travel, get off the train and get to the next hotel. That said, I would spend my time in Amsterdam, London and Paris and cut out Brussels and Bruges. There is so much to see in all three cities, and with kids they won't be bored seeing the Tower of London, Big Ben, Eiffel Tower, plus there are tons of museums in each city to see. It takes time to go to museums, walk the streets, have breakfast, lunch, dinner. And in Europe, they take the time to sit at an outdoor cafe and eat lunch. Part of the experience. Takes time to get from site to site. It takes time to tour the big sites and then happen upon something and spend time there and by the time you know it, it is time to leave. I would definitely recommend going to the libarary and getting out travel books including the RickSteves books on each city. Watching YouTube free videos of RickSteves and others about each city. Looking at the online Rick Steves scrapbooks. This way you will know more abut the major points of interests.
You want to take them to some art museums, in Paris, the Lourve, the D'Orsay. Les Invalides where Napoleon is buried, very cool. Notre Dame church, need to make reservations for the Eiffel Tower on line way in advance. Buy the museum pass, see if it is worth buying if you are going to several museums. It will help you not stand on long lines. Visit the Arc De Triomphe in Paris, go to the top to view the city and see the Eiffel Tower in the view. Great to do at night and during the day.
In London, St Paul's Cathedral, maybe take the time to tour Windsor castle. Start with the travel books, YouTube Videos and then figure out what you think you would like to see and do. Then come back to the forum and ask more questions. As for Amsterdam, tons to see and do there too. Anne Frank house and walking around seeing the canals, canal boat ride during the day and at night and of course the major museums. I hope this helps you get started with your planning. In London, you may want to buy tickets to see a play or go to a church to hear Evensong.

Do you already have your plane tickets? If not, I would fly into Amsterdam then take the train to Paris and then take the train to London and fly home from London. The train ride from Amsterdam and Paris is not too long and easy to do. And I think it would be easier to take the train from Paris to London then from Amsterdam to London. This is something worth checking out, as you want to travel the least amount of time from city to city.

Yes, I already have my planes tickets. I can definitely take Brussels out of the itinerary, but would still like to see Bruges. I'm planning to see Les Miserables while in London since that's a bucket list item on my list.

Amsterdam, Paris, and London are three of Europe's greatest cities, meaning you will not run out of things to see there. With only two weeks, you may find it hard to see and do everything you are interested in. I don't suppose one night in Bruges will make that big a difference, but if you want a diversion in a quieter, charming village, you can find that on the outskirts of the big cities, easy day trips, without making a stopover for a night. Bruges is lovely, but it is very crowded with tourists in the summertime, and there are equally lovely places near Amsterdam (Haarlem, Hoorn, Edam, for example, but there are many others) that will give you a break from the hubbub of the big cities and won't require you to change hotels.

Also, you have two teenage kids who I'd recommend you get involved in planning this. They are more likely to be engaged if you give them each, say, one or two days to plan.

Given the number of major sites in each, I feel like you've got, comparatively speaking, too much time penciled in for Amsterdam (4 full days plus your arrival/jet-lag day) and too little in London (2 full days plus perhaps one partial day) and Paris (3 full days plus perhaps one partial day). Unless you're planning out-of-town trips in Amsterdam but not in London or Paris, I believe you'll need less time in the first city, whose tourist zone is smaller, and where you may well need less time to reach your hotel for initial settling in.

Because you are focusing on major cities, you are right to use trains. You will need to buy Eurostar tickets when the window for that time period opens, but before the prices start to increase towards actual travel months. Of course, that means NON CHANGEABLE, Non-refundable tickets. And it adds up for four people. You should learn about "Any Belgian Station" tickets if you keep Bruges in the mix.

I agree that you can drop Brussels, unless you want to see the excellent art museums there. But there's a Eurostar to London from there, and it doesn't stop in Bruges, it stops in Lille, France. Have you investigated low-budget airlines to get to and from London? (Fees, luggage rules, and alternate airport usage, pay attention.) Personally I would leave out London, but it's not as easy from PR as it is from the 48 states, I agree. Brussels, Bruges, Gent, and Antwerp add up to one big city in other Euro countries, and local trains are cheap and easy, if you decide to keep Belgium.

You should not rely entirely on internet advice for your first (???) trip to Europe. There are too many things to decide about and to see. One source I like are our host (Rick Steves) guidebooks, which you can read in libraries if you don't want to buy them. You could say he specializes in travelers making their first trip to a country or area. He also has free travel advice (like for trains) on the main part of this website.

I have already ordered a couple of Rick Steves' books for Amsterdam and Paris. Haven't received them yet though.

"You should not rely entirely on internet advice for your first (???) trip to Europe. There are too many things to decide about and to see. "

This I so agree with. This forum is good about answering the questions asked, as well as about pointing out obvious possible monkey wrenches. But we are not mind readers, and there could be some wonderful sights near a traveler's target area that would mesh brilliantly with his special interests, yet we'll likely never mention them. That's where guidebooks are so helpful.

I'm not a big fan of TripAdvisor, but scanning the top attractions for a city can turn up things that don't make it into most guidebooks, one or two of which might be exciting to any particular traveler.

We have been to all of the cities except London with my boys 13 and 15 in the last 2 years. Things they loved were biking around Amsterdam and Bruges, Ann Frank house(reserve tickets ahead), canal boat in Amsterdam, taking the high speed trains, in Paris the Eiffel tower, climbing Notre Dame, boat on the Seine, Arc de Triomphe, going the markets, Musee d'Armee, our day trip to Normandy for DDay beaches, and in Bruges and Brussels just walking around, and food everywhere. I would agree on maybe less time in Amsterdam, unless they are really into art museums or maybe bike trip in the countryside. The one thing with boys that age depending on their taste is they can get overdosed on art museums and cathedrals. I also highly recommend going to the library and getting multiple travel guides which have different strengths to allow everyone in on the decision making process so the kids are invested in what you are going to do.

July 8 Arrive Amsterdam (3N)
July 11 Thalys to Paris (4N)
(July 14 celebrations in Paris)
July 15 Eurostar to London (3N)
July 18 Eurostar to Brussels (3N)
(days to Bruges and Gent/Antwerp)
July 21 Train to Paris CDG (1N)
July 22 Depart Paris