Planning a 10 day Itinerary starting and ending in Amsterdam

I took my 13 yr old daughter to Amsterdam, and she enjoyed the Anne Frank House, the Heinekin Brewery tour, wax museum, and the Amsterdam Zoo. At the zoo, see if you can be there when they feed the seals. You can see a typical session by going to Youtube and looking for a video called "seals in the Amsterdam zoo".

I'm curious why you chose Prague. Interesting, though I don't recall much for kids. However, if you do go there, take a 40 min train ride to Kutna Hora, home of the "Bone Church". Google image it.

Actually, the nearest "big town" is Paris, which I think has lots for kids: climbing the steps on the Eiffel Tower, going to the catacombs, take the Sewer Tour, climbing the bell tower at Notre Dame. There's also a book out there called "Take the Kids Paris".

I could suggest some cities in Belgium - both Bruges and Ghent are delightful, plus they're all in the same general location. I don't think a lot of train travel with 6 would be easy or pleasant, but short jaunts you could do. I also like the idea of Paris.

I could suggest some cities in Belgium - both Bruges and Ghent are delightful, plus they're all in the same general location. I don't think a lot of train travel with 6 would be easy or pleasant, but short jaunts you could do. I also like the idea of Paris.

With only 10 days, and the requirement to return to Amsterdam, you don't have time go to as far as Prague on this trip.

Remember that the larger a group, the slower it moves (yours is 6 people), and a group only moves as fast as its slowest member (this will vary, but with 6 people, someone or other is bound to not be ready to move quickly at any given time). Therefore, I'd minimize changes of cities and hotels. This also means you shouldn't plan too tightly, but allow slack time in each day.

Given all that, I'd stay in the Netherlands. There are plenty of smaller cities and rural destinations easily reachable from Amsterdam, either as day trips or overnights. If you get Rick's Netherlands book, he has details of lots of options, complete with goof-proof directions on seeing these places from Amsterdam.

There is indeed enough to do in the Netherlands to fill your 10 days.
Consider staying a few days in the eastern part, such as Zwolle. A good base for visiting the lovely nearby cities on the river IJssel and for cycling trips.
You can also consider not staying in Amsterdam itself, but in smaller cities around. Haarlem is getting a popular alternative, but historical towns as Abcoude and Weesp are also suitable places to stay with a family like yours. All have perfect rail connections to Amsterdam (20 mins or less), and with countryside around the corner.

I agree with Tom. There is plenty to see and do in Amsterdam and day trips aplenty. Try and go to Edam on a Wednesday when they have the cheese market (go early for best seat). I know, cheese market sounds boring, but it is anything but. Everyone is dressed in traditional clothing, there is a band, children, adults, everyone participates. We then got some cheese, bread, and drinks and had an impromptu picnic. Also, Check out localbus.nl, also mentioned in Rick's book. It has different routes to smaller towns and is very inexpensive and easy to follow. That's how we got to Edam.

Also, Amsterdam has the Dutch Resistance Museum which has a section from children's perspective during the war. It is right near the zoo. The maritime museum has a replica of a Dutch East India ship you can explore which might interest the kids. We didn't make it to the science museum but that is also geared towards kids. We spent 9 days there and didn't get to everything on our list.

... and end your trip in Utrecht. Wonderful, lively historical university city, birthplace of Miffy (in case you have enthousiasts in the family; locally known as Nijntje), 30 mins by direct train from Schiphol airport, and another good base for day trips (the fortified town of Naarden, the river port town of Culemborg, the castle in Amerongen, and what not).

It's easy to day-trip around the Netherlands. I agree that you don't want to change hotels a lot, but do consider one additional base besides A'dam, unless you get a really good deal on an apartment there. Your family might enjoy a day at Madurodam. The Maritime Museum in A'dam is very interesting for kids and adults.

You'd be better served in terms of efficiency by flying into Amsterdam and out of another city, or vice versa, if you want to see other places such as Prague. It will save you time by not having to backtrack.

Any recommendations on a possible itinerary would be helpful.

You shouldn't overdo it, but f you want to travel a bit, why not? I mean, look what Rick Steves' tour from A'dam does with only four more days than you have:

https://www.ricksteves.com/tours/europe/family-europe-amsterdam-rome

A similar pace would probably be too much. But you could easily handle a side trip into Germany and back. Bacharach (that first stop on Rick's tour) is in the Middle Rhine Valley, an outstanding place to see the countryside and enjoy small, old-world towns, castles, great scenery, and a few diversions. Leave A'dam at 8 am by train, arrive 5 hours later in Bacharach.

These pages should give you an idea of this area:

https://upload.wikimedia.org/wikipedia/commons/4/4c/Bacharach_BW_9.JPG

https://c2.staticflickr.com/8/7350/9674920482_e2743ed02b_b.jpg

https://www.youtube.com/watch?x-yt-cl=85114404&x-yt-ts=1422579428&v=qxFF80wORNQ#t=32

http://schnuggel-elsje.de/upload/Bilder/IMG_0131.JPG

https://www.tripadvisor.com/Attraction_Review-g198627-d3306006-Reviews-Sesselbahn_in_Boppard-Boppard_Rhineland_Palatinate.html

http://www.bingen-ruedesheimer.de/wp-content/uploads/2012/10/LZ1B0487-als-Smart-Objekt-1.jpg
http://www.marksburg.de/en/circuit/

http://www.staedte-fotos.de/1024/sankt-goarshausen-altstadt-burg-katz-23553.jpg

https://www.youtube.com/watch?v=3cmXwJNvFg4

http://www.deutschlandgourmet.info/bilder/gross/5710-Restaurant-Weinhaus-Heilig-Grab-Boppard.jpg

http://www.der-takt.de/typo3temp/_processed_/csm_RS4284_rpt-2010-rad-rheintal-057-brey__blick_auf_marksburg__rheinr_Dominik_Ketz___Rheinland-Pfalz_Tourismus_GmbH_13151d4098.jpg

I like the idea of going to Bruges and Ghent with Amsterdam, BUT you could certainly find plenty to do in the Netherlands for 10 days. From another mom with 3 kids ages 10-15, there's:
Edam/Voldenam/Markham: https://www.ricksteves.com/watch-read-listen/read/articles/going-dutch-on-a-day-trip-from-amsterdam
Kinderdijk: https://www.kinderdijk.com
Zaanse schans: https://www.google.com/search?client=safari&rls=en&q=zaanse+schans&ie=UTF-8&oe=UTF-8
Kroller-Muller museum (the second best collection of Van Gogh after those in Amsterdam, located in a park where you can rent bikes and ride throughout): https://dutchreview.com/featured/the-kroller-muller-museum-a-day-of-great-nature-and-van-gogh/
And throughout the Netherlands, biking is a great way to interact with the cities and countryside.
In Amsterdam, don't forget the NEMO children's science museum, which may be a little young for your older kids but has a wonderful roof-top deck where you can drink a beer while your kids explore the museum
Also, the Old Church in the Attic is a wonderful close-up experience of a specific time and place in history...

I could add many more...