iAmsterdam card

You're gonna have to crunch the numbers to see if it will save money in your situation, but in general if your visit two covered attractions and ride the trams/metro four times in one day you come out ahead. Since you will be traveling with children, there may be interest in visiting the city zoo. It's the most expensive attraction in the city, but fully covered by the card! If the zoo was already on your wish list you'll save big bucks with the card. All details can be found here:

http://tinyurl.com/zczjpoh

We used the card there but Michael is right - add up the entry costs for you site and see if it pencils out. I almost always buy a city card if I can find a comprehensive one. I love the freedom of feeling like I already paid so I might as well stop in, even if it's for 30 minutes. We used it to go to the zoo, which made it an easy decision for us. The zoo was pretty cool - the lemurs are loose in this area you can just stroll through. I loved it!

I found that the Museumkaart was a better buy for me- does not include the transport pass but the numbers still worked out better overall for what I wanted to see.

As far as what comes with the card:
http://www.iamsterdam.com/en/i-am/i-amsterdam-city-card/what-is-included

Here are the Amsterdam attractions covered by the Museumkaart: http://www.amsterdam.info/museums/museumkaart/

It's a particularly good deal if you are going to other places besides Amsterdam, as it covers admissions all over the country. I got about one and a half times the purchase price from mine. As said above, though, you have to crunch the numbers for what you intend to see.