What I would recommend is that you google European RV trips with kids or find a forum for travellers with kids in the areas you want to travel in. There is a lot of info on the internet if you have the time and it looks like you do.
Our trip with our 2 boys(same age as yours), was Feb and part of March/92 in a small "C". Travelled from London through France, Belgium, Germany, Italy, Spain, Portugal. No campsites open but we felt very safe camping anywhere so I don't think that there would be any problem if you do not get a spot in a CG. Remember, you will be in the high season so campgrounds, especially for something as large as a C and anything around water, will be tight for spaces.
Parking can be a real problem for bigger RV's around larger centres so you might be wise to park in a small village in the rural area and take a train into the centre of the city.
1) It is possible to see the places in your itinerarty in 21 days but be flexible if you find that things are not going as planned.
2) The more you can expose your kids to travel and things different than their regular routines, the better they will be able adapt to our changing world when they are older.
Our kids still remember this round the world trip to this day.
3)I am familiar with 1,2,3,10,11,12.Venice is pretty crazy with people in the summer but it does have good beaches for the kids close by.
We were in 1 and 2 this summer all interesting. 3 a few years ago. Lots of interesting architecture.10 is a mellow place to visit, 12, is a large lake and great campsites and water sports and warm weather.
4) We were in Europe for 2 months this summer and although we stayed in campgrounds, I would feel safe free camping in any of the countries were were in(Germany, Austria, Slovenia, Italy, Switzerland, France), if you could not find an available campsite.

Our little "C" in Cervinia(Italian side of the Matterhorn)

All of the Crosschecks RVing across Europe.
Have fun.
Dave