That's a pretty wide-ranging travel plan for a short period of time. DH isn't being spared much driving with this plan - it's about 700km of driving without detours, boys in the back seat...
Not sure what to advise you about the number of nights in each place. It depends on why you're going where you're going.
Remember that with 4 people, every move is a small crisis. The packing and unpacking routine must be timely and coordinated and will be cumbersome with 8 travel legs in 11 days (8/18-28.) You must also find your hotels and new parking places, and check in and out 8 times.
I think it would be wise to ask how you are expanding your experience with each of your 8 travel legs. I'd be happy to bet that you could accomplish the same experience with half that many legs and fewer miles. You are anchored by Frankfurt. Look at your most distant destinations first. What is so vitally important about Munich, Nuremberg and Salzburg, or even Füssen? These are nice places, but they aren't enjoyable if you are racing around. What if you stuck to a Frankfurt - Lindau route and stayed in just 3-4 places? That's a lot less time in the car, but you wouldn't be cheating yourselves. If you travel as far as Lindau, you are spitting distance from the Alps already. Stay in Lindau 3 nights and maybe take short day trips to Appenzell, CH (see Rick Steves on this) or to Oberstdorf (famous alpine ski jump, nice town) or perhaps to Füssen. Visit the Zeppelin museum in Friedrichshafen (a "boy" thing maybe) and take a ferry across Lake Constance In between, you visit Heidelberg and Stuttgart.
Staying in a castle: Your best shot is probably right near Frankfurt in the Middle Rhine Valley where there is a cluster of several castle hotels and castle hostels:
Burg Reichenstein
Burg Gutenfels
Burg Liebenstein
Schloss Rheinfels
Auf Schönburg Castle
Bacharach Castle Hostel
Diez Castle Hostel (east of the Rhine on the Lahn River)
I suggest you stay 3 nights on the Rhine anyway. There's a LOT to choose from for families. Rheinfels Castle. Marksburg Castle tour. River cruises. A summer bob run in Rüdesheim (Loreley-Bob.) An amazing open-air museum in Bad Sobernheim. You can visit the WW II site Bridge at Remagen Museum. If you think a Holocaust / Nazi lesson is in order, the Documentation Center in Cologne could be a day trip (See the cathedral too.)
So I'd suggest this in this order...
Stuttgart (2-3 nights)
Lindau (3 nights)
Heidelberg (2 nights)
Rhine Valley (3 nights)
From most towns on the Rhine you can get to FRA easily on the morning you leave.