In reply to Sam W:
Depending on what type of campsite you're after, maybe have a look at https://www.natuurkampeerterreinen.nl/en. They're a certification body for more basic/nature campsites. The search function on their website is quite good, e.g. you can select campsites that have a place to swim (river, lake, sea) within 1km of the site, sites with bad weather cover, etc..
You could also take a look at https://www.trekkershutten.nl (I couldn't get the map search function to work on the English language version of the website, but it should work if you switch to Dutch). They're basic 'hikers huts', spread across the country, often located on campsites. Prices start around €40/night.
As others have said, Hoge Veluwe is very nice, but fewer swimming opportunities (although there will be plenty of large campsites that have swimming pools). The north (either Frisian islands or Friesland) is also nice, and lots of water (sea, lakes, rivers). Loonse and Drunense dunes is also a lovely area, and de Efteling is a great theme park with plenty to do for small kids (but expect it to be very busy during the summer holidays). I'd avoid the far South of the country (near Maastricht), it's beautiful but surprisingly hilly with lots of short sharp climbs which may not be ideal for the kids.