Not sure if this is much help but have got to know Amsterdam reasonably well over the years having lived there twice. Although dd was born there we moved back here soon after so didn't do much "kiddies" things but the Dutch are very into their children and Amsterdam has soooo much more to it than sex and drugs.
- Get away from central station, this is all too often the first and sometimes only glimpse of Amsterdam that people get there is much much more.
- Depending of course on your kids ages hire some bikes, cheesy yes but definitely the best way to see the city. (They should have an option for kiddie seats also)
- The canals are great for some sightseeing too and depending on your ambitiousness you can either join the throng on a barge or hire a mini boat (not sure of terminology) with a small motor and cruise at leisure.
- Museums are a plenty, Art, History too many too mention. Get a guide and choose what's best for you. The Artis Zoo is the oldest zoo in Europe and has kiddies playground too, thousands of birds and animals, well worth a visit. There is also a Kindermuseum (childrens museum) but I think it's aimed at older kids.....not sure.
- The Vondelpark is huge and beautiful and also well worth a visit if only to let the kids run around a while, don't remember seeing a playground though.
- Delft, Utercht and Leiden are all nice day trips but dependent on your time and length of stay.
- Can't really recommend anywhere to stay sorry but just stay away from central station, anywhere around the Vondelpark would be nice.
The Dutch are a quirky people, not at all what you expect when you get to know them, They're a blend some say of liberalism and conservatism. The liberal I don't know, more tolerant in my opinion but they do have a strong sense of family and most restaurants will look after children well.
It is a very pretty city and perfectly suitable for children once you avoid the obvious, so don't let anyone tell you otherwise.
Sorry if this is long but someone has to benefit from my insomnia