Sounds wonderful!
I think you might want to plan to visit fewer countries given you have 4 weeks, although it sounds a lot you will cover a lot of miles and time trying to do all those. What unit do you have for camping? If it is a motorhome/trailer/caravan you might find tolls/ferries much more expensive as well to cover the different countries. If you just have a car, then I would really consider using the ferries/bridges, rather than driving the long way around as although they are more expensive you will get to see more (and they're an experience in themselves).
What kind of places to visit/things to do are you keen on?
Netherlands- we have camped in 3 places here, Haarlem, a place near Deventer and near Breda. We found places using this website. We visited Harlem, Amsterdam twice, Enkhuizen outdoor museum, Hoge Veluwe, Deventer but also chilled and mixed with others (mainly Dutch) on the sites. We found visiting attractions tended to be a little more expensive in the Netherlands as they tend to charge for children. Food about the same as here. though it can be tricky using foreign credit cards, and traffic about the same too.
Lovely campsite
another one
We're camped more extensively in Denmark, campsites are great and very family orientated. School holidays are from June- beginning of August, so can be busy but you should find somewhere. A lot of sites have little cabins to rent, again these will be easier to find for the night from the second week of August onwards.
My highlights of Denmark are
Skagen (a long way, but so worth it and if you're thinking about Norway, you could catch a ferry near by at Hirtshals),
Aarhus/Ebeltoft- again you could catch a fast ferry over to Zeeland for Copenhagen
Aero- but probably only for a daytrip- ferries are expensive unless you'll stay there a week.
Copenhagen- spend a few days here, and visit Roskilde, Helsingor from here. Love love this camp site but book this if you go before the middle of August. A copenhagen card is good value for families as it includes the kids and transport, if you can start the card half way through the day to get extra value from it. Go here!
Bornholm - lovely island in between Sweden and Germany, may be useful as a route out/back.
Sweden- we've camped less so here. When we went we felt we had 2 choices, as we had a week, either go North from Malmo (towards Gothenburg) or east (towards Karlskrona). We did the latter, and came back via Ystad for Bornholm. It was ok but Denmark had more appeal for us.
Hope this helps a bit- do come back with any questions about the above, or any others and I will try and do my best to help.