We've been to the Netherlands every year for the last 5 years (kids are now 6 and 8) because we love it so much! We've never been camping there, but have stayed in bungalows in holidays parks, some of which also have campsites. The company we've used every year is called Landal Greenparks, and they have a whole chain of sites across the Netherlands and other countries. Some of them are ex-Center Parcs sites, so have great swimming facilities as well (we went to Het Vennenbos this year, but we've also been to Coldenhove and Twenhaarsveld). Many of the sites also have a leisure centre attached, where you can do tennis, basketball, etc. And we always hire bikes and use them to explore the surrounding area - the Dutch cycle network is amazing! A budget of £2k is very generous: we usually spend about £400 on a bungalow for the week, £300 on travel, and a few hundred pound more on food, activities, etc. It's a fraction of the price that Center Parcs in the UK would be, even in the school holidays! And if you're camping, obviously that would be even cheaper.
We live in the East of England, so we've usually got the ferry from Harwich overnight, as Zipity says. It's a brilliant way to travel - the kids are always very excited about having a cabin to explore, and you arrive at about 7am the next morning, so you can arrive at your site by 9am (NL is very small, so you're never more than a couple of hours' drive from Hook of Holland!). I think it's usually about £300 for a return single car ticket with family cabin, but this varies according to the time of year. The cabins sell out very quickly, so we had to go via the Eurotunnel this year instead. That's also ok, but involves much more driving (for us, anyway).