There probably will be rain, but there may also be really nice days. As it is unlikely to be really busy, you can wait to closer to the time before booking any campings. I would also take an electric fan heater so you have safe heating for during the nights (I am always really wary of leaving the gas heater on during the night when camping) and the campings will obviously have an electricity supply. If you bring your own coax cable (and TV of course) then many campings will be able to provide cable television as well.
If it looks that the weather will be reasonable, then depending on the age of your children Noordwijk or Katwijk may be nice. Next to the beach. Noordwijk is quite nice, reasonable shopping, nice restaurants ('Het Galjoen' is excellent). You would be close to the Space Expo in Noordwijk (nice, but not as good as the Science museum in London). Also close to Leiden, which is pretty and has many nice museums and Delft (again nice city, nice museums, you can climb the bell tower of the New Church, which still dates back to 1280 or so, so not very new). You would also be close to Duinrell (very expensive, but quite nice). You could also easily make a daytrip to the Efteling (much better than Duinrell imo).
Alternatively you could go to Drenthe. I would like to recommend camping Witterzomer near Assen. Very nice, good facilities (although we were there during Summer), close to Verkeerspark Assen (nice for kids up to 8-10 years or so).
All in all, I think it is possible to have a good time, but it would be much better if you have good weather.