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.
We went to Duinrell (sp?) about three years ago in early April. Great waterpark, small fairground and also close to the lovely city/town of Leiden. We were able to take day trips to Hague and Amsterdam. It was different to normal holidays we take (France/Spain/Italy) but none the worse for that - some great memories.
We went to Beekse Bergen in Nord Brabant last Easter and had a great time despite almost constant rain and chilly temps - I think we had about an hour and a half's sunshine in the 5 days we were there and I wore 2 pairs of pajamas some nights. We were in a Eurocamp safari tent which is raised off the ground and wished that we had taken wellies as the route to the shower block was several centimetres under water at times. That said, the weather might be brilliant this Easter (remember the gorgeous week we had in March 2012?) so I wouldn't say it was mad, just a bit risky perhaps. Depends on what you plan to do when you're there I guess... at Beekse Bergen you can pay for an Extra Card which gives you unlimited access to the attached safari park (much better than Longleat) and Speelland (a small scale amusement park for 3-11 year old) as well the Sportiom swimming complex in Den Bosch (like a Centre Parcs one, 30 mins drive away) and some other attractions. The site itself is a mixture of Jungalow chalets, statics and pitches and has it's own indoor pool complex with a particularly good shallow pool. You're also not too far from Antwerp, Eindvoven and could even get to Amsterdam as a day trip. De Efteling theme park is just down the road. We're going back again this year, but not until early May and in a caravan.
Is this do-able? Anyone done it? Any recommendations? I'm not expecting scorching weather at easter BTW but it'd be nice to hear from anyone who has been at easter and if so, where they went etc. I bought a trailer tent last year and we've only used it once for gawd's sake . Ta in advance