London to Amsterdam to Frankfurt opinions

I think it's fine, but I have a LOT of questions about why Amsterdam and even more about why Frankfurt.
I LOVE Amsterdam, but I wouldn't take kids there if they're too young for Anne Frank House. And if they're all pre-teens (unless they are 12yoa triplets), they're too young. Better to take them when they are old enough. Instead, consider Belgium. You can take the Eurostar to Brussels and then head to Bruges or, better yet IMO with kids, Ostend or DeHaan on the coast. The tram that runs along the coast connects you to the Atlantikwall Museum to the west and an aquarium (which I found out about later) to the east. Day trip to Bruges for the canals?
I have taken to flying in/out of Frankfurt, and I build my trip around that flight. Last summer, we stayed 1 night in Wiesbaden (recovery in the thermal pools!), then 2 nights in the Mosel Valley, which is very close by and not another big city. You don't have to have a car in this area, but we really liked having it, as it gave us more options. There are trains and boats and bikes that you can take to castles, both intact and ruined. Gorgeous area, well worth the visit.
Another option is an even split between London and Paris. You can't go wrong with those two.

maschuld,
It is doable. Be aware that your 4 nights in London means only 3 full days there. Likewise you have 2 full days in Amsterdam and 3 full days in Frankfurt. Personally I would pick a different city in Germany (I am very fond of Munich), but Frankfurt has many things to offer. If your flight home must be from Frankfurt, the train from Munich to Frankfurt takes just over 3 hours, plus add on time to get to the station, etc. Maybe stay the last night in Frankfurt after an afternoon train from Munich.
It appears you have 11 nights on the ground, 3 days changing locations and 8 days seeing the sights. For me, I would drop one country. Even pre-teens will get tired of moving every 3 or 4 days. (We have taken our kids and grandkids to Europe, mostly France, also when they were preteens and teens.) Split your trip to 6 nights in London (with 1 or 2 day trips perhaps) and 5 nights Amsterdam. That gives you 5 days London, 1 day transit and 4 days Amsterdam. You will not run out of things to see and do. Or do London and fly to Germany for the second part of the trip. It's worth considering.

Just fyi, check the England section and search for things to entertain the kids. London has tons of things they will like (even some of the museums will interest them). Also, Munich, IMO has many things to appeal to kids. Check the Germany section also, and Netherlands for ideas for the family. There are lots of nuggets provided by the forum members.

Best of luck for a wonderful family trip!

Thank you both for the quick replies. The only reason I considered Amsterdam is because it seemed like such a cool city and so easy to visit when I was there about 10 years ago--the canals, the bikes, the trains. I remember being a bit amazed by the day-to-day there. I never ended up visiting the Anne Frank house simply because it was such a long wait. I do realize there may be a lot of other themes in Amsterdam that might not fit their age range but it seemed pretty easy to avoid these areas. Based on both your suggestions though, maybe Amsterdam would be worth saving for another time so we can not be so rushed to leave London.

I apologize for not elaborating on Frankfurt. We don't intend to stay there but it is where we are meeting friends who live outside of the city. I really appreciate the suggestions on where to visit/stay as I think we'd be in smaller towns or the countryside. I have to do far more research on this portion of the trip.

It sounds fine, those three spots work well, they mean something to you, so go for it. Suggestions you get about going somewhere else will just confuse you, and soon you are into analysis paralysis.

In 10 or more days, you are not really moving that much, London to Amsterdam is a morning train ride, 4 1/2 hours, you get to Amsterdam in time to check into your hotel.

Amsterdam is fine with kids, not sure of your plans, but just wandering the canals, maybe have some street snacks at the Albert Cuyp market, take a canal boat tour, then museums as their interest warrants. I think the Rijksmuseum is good for kids, might have to coach them through some of the masters, but they have most of the top pieces in one hall. There are also some other galleries, with ship models and other objects they might find interesting. The Van Gogh museum might be a bit esoteric for preteens, the Anne Frank house OK, it probably means more to you than them, not sure if even the diary is required reading in schools like it once was, which drove most of the fame.

Frankfurt is only another 3 1/2 to 4 hours, again, you get there plenty early in the day.

For both journeys, book your tickets well ahead. For London/Amsterdam, Eurostar ( https://www.eurostar.com/us-en ) is what you want to look at, just when you pick your departure time from London, remember that you need to get from your lodging to St Pancras station, then be there well ahead (At one time 90 minutes, maybe 70 now, when you book they will say). So if you are relying on the tube, be conscious of when trains start.

For Amsterdam/Frankfurt, you can book either through NS International, ( https://www.nsinternational.com/en ) the Dutch rail carrier, or Deutsche Bahn https://int.bahn.de/en the German Rail company.

We were in Amsterdam with our kids and grandkids 10 and 7 at the time, last summer for 5 days. They loved it. Although the 7 year old was a bit young for the Anne Frank House, the 10 year old grandson who is into everything WW2, was totally interested. They loved the canal ride, the day trip into the countryside to see the windmills, and the freshly made stroopwafels. And the Rijksmuseum had one room of old intricate dollhouses, the granddaughter was fascinated with them.

Re: Anne Frank House. The book may not be required reading in school, but it is worth reading. I re-read it before I visited Amsterdam the first time. The museum does a great job of presenting Anne's story in context and in a very accessible way. The Museum has a minimum age of 10. You know your children. If they are mature enough to handle it, it is well worth the visit. There's no more waiting in line these days. You have to book ahead, and in summer, slots go quickly, so make sure you know how to book and mark your calendar. Here is what the Museum says about visiting with children:
https://www.annefrank.org/en/museum/practical-information/visiting-with-children/