You have done good preliminary work and you should be able to organize this yourself with help from this board. No need to pay a commission to a TA. Remember, when booking flights that you can fly "open jaw" (into one place and home from another for no extra cost) to save time and money backtracking. For example you could fly into Amsterdam and home from Paris or Frankfurt. If you have 16 or 17 days, I would limit myself to 4 or five places, remembering that it is easy to do day trips by train. Also, I like to plan for an easy orientation day when I first arrive and am jet-lagged. Being able to walk a bit in the sun to get your body attuned to the new time zone, enjoying a leisurely lunch and some people watching would do the trick. Trying to absorb all the sights in a museum...not so much.

Germany and the Benelux fit your plans better than a place like France because train travel in the French provinces is not that convenient. I would recommend the Dordogne or the Provence in France, but I think that a car is necessary for that. On the other hand, Rothenburg, small German cities, almost any town in the Benelux is readily reachable via public transportation. In fact, when in the Netherlands (a long time ago) we took the train from Amsterdam to Haarlem, the Hague, Enkhuizen and other locations with no more problems than if we were taking the subway in NYC, and the ride was no longer than going to Manhattan from the outer boroughs. I rule out Switzerland because of the cost.

We did this when our oldest graduated from high school, so about the same ages. Shopping was important--for boys and our girl--sporting goods are beautiful!! We drove for part and trained.
We landed in Luxembourg on Icelandic, and made a loop back to Paris.
Your air fare in June is going to be prime time--you don't say from where.
We stayed in a castle for a night (and I'd have to go look to see where--but it was German and with a vineyard).
If I could make my arrangements BEFORE the internet, you should be able to now using it!!
Our children were all Latin students so incorporating Roman sites was part of our planning. Maybe your kids have some similar interests.
Is there a reason driving isn't a part--I think it can be very economical for 5 and makes for interesting stopping, picnicking, etc.
Good luck and come back.
I am going to put in the idea of hiring Michael Osman as a guide for Paris right now. It will be the best money you spend for "bang for the buck".

Looks like a good basic plan. Given your interest in a bunch of countries I would look at a central tour that goes something like

Fly into Paris, a few days enjoying the city, Giverny and Versailles should do
Trip to Strasbourg, days out into the Black Forest and onto the top of the Vosges.
Follow the Rhine to the Start of the Mosel (pop up the Mosel and stay in a little town with a castle, vinyard, pool and hire bikes)
Amsterdam, you can stay in the city centre but you can also stay in say Haarlam and catch the train in to visit. Hire bikes and get out and see the countryside.
Then fly back out of Schiphol

Use bahn.de to get a good basic idea of continental train systems. Then once the basic plan is sorted have a look at local country train websites.

Have a look at
http://www.otstrasbourg.fr/?lang=en
http://www.mosellandtouristik.de/en/

I guess you know about seat61.com it explains about the train systems