Hey, we did a 4 month round trip - UK, Belgium, Luxemburg, South Germany, Switzerland, Italy, Austria, Czech, Italy, France, Spain, France and back to UK last summer. It was great - you will have such a great time.
I will try and find our diary to recomend specific campsites we liked, but will have to do that tomorrow.
Off the top of my head - Switzerland is just SO gorgeous in every way. Ignore anyone who tries to tell you its 'too expensive' - we didn't find it more expensive (apart from the fact that we chose to do some expensive activities - cog railways, cabel cars etc) - meals etc seemed the same as anywhere else.
We stayed at the Jungfrau campsite in Lauterbrunnen and it was lovely - it wasn't the cheapest site we stayed in (although also not the most expensive), and the facilities were very good - family bathrooms etc. I don't know if they have cabins, but did have tents you can hire.
There is a fab (free) mountain pass from Switzerland into Austria - we stumbled upon it and has some of the best views of the trip...I will try to find the name.
We stayed in a site we liked in Luxembourg - had a nice playground (again, I will check the name) - Right in the middle of Lux there is the most amazing playground we've even been too - it really is worth visiting - my kids spent hours there but could have spent days! And we liked the city too.
My top tip for travelling with kids (although sounds like you've already done a bit) is to plan to do very little, and expect to do even less than you plan. The travel itself is half the experience, and chilling out in a town souaking up the atmosphere is just as worthwhile as seeing 'the sights'.
I'll be back...