21 day trip in June 2015

On your current plan, Prague to Wurzburg takes 5 hours by bus and train, so you'd only have about a half day to visit Rothenburg, then you'd spend a lot of the next day driving to Fuessen (3 hours with no stops, but the point is to make stops). I don't think you'd see the main castles around Fuessen unless you spend another night.

Skipping the Romantic Road and taking a train or bus (also operated by the railway) directly from Prague to Munich cuts that travel time down to 5 or 6 hours. You could either continue on to Fuessen the same day and sleep two nights there or stay longer in Munich and day trip to Fuessen.

I don't usually recommend one-night stays, but you have a good mix of several nights in each place surrounding the two one-nighters.

As a family of adults, I assume your group will be less unwieldy than some other configurations. What does your daughter suggest you cut out or trim back?

Sorry,, I totally agree with your daughter..

One night stops are not "visits" they are just transit.. if a place is worth seeing .. then isn't it worth one FULL day at least.. which means TWO nights.. if a place isn't worth a full day then to me its obviously pretty low down on wish list.

Two nights equal one full day..

Well, for your group to have time for seeing the Alps at southern Germany, I suggest : delete Rothenburg from your travel plan. Ride in a train from Prague to Munich. Rent a car at Munich, for you to drive to the Alps mountains region near the border of Germany and Austria. You could stay at a hotel at Garmish two or three nights. (that is what I would do). Drop off the car at Munich, and ride in a train from Munich to Salzburg. I would want to be at Venice 2 nights. And be at Rome 5 nights. After all of that travelling, I think you would like to stay at one place for a while. From Rome, you could go on a day trip to Orvieto. You could have 3 whole days at Rome, plus one day for a day trip. Three whole days at Rome could go like this :
Day one : Vatican.
Day Two : Ancient Roman Forum, Capital hill, Pantheon.
Day Three : Villa Borghese gallery (white marble sculptures by Bernini). Ride in a Taxi car from there to the Spanish steps. Walk to Trevi Fountain. For a group of five adult persons, I think the rental car in Germany should be a Volkswagon micro bus.