"With traveling with two kids by myself, I want it to be easy to get tickets, etc."
I think this is a very wise consideration. It is indeed pretty easy to use ticket machines or to buy tickets at a counter (English skills are commonplace among DB customer service agents) in Germany IF you know what tickets you are looking for. Railpasses simplify things as well - but the expenses do add up.
"We leave Prague on a Sunday and fly out of Frankfurt on Friday."
The trip from Prague to Munich is typically accomplished by IC Bus these days:
http://www.bahn.com/i/view/USA/en/trains/overview/ic-bus-prague.shtml
This cuts roughly an hour off the travel time, but it's still nearly 5 hours to Munich.
That means you will have a few hours on Sunday to check in and see a little of Munich - and then 4 days to see a little more of Munich, to travel to Füssen and do the luge (again nearly 5 hours round trip travel time to Neuschwanstein, which is NOT a castle,) to travel to and visit Rothenburg (3-3.5 hours on the train,) to travel to and visit the Rhine (4.5 hours to St. Goar) and then make a final train journey to the airport. I do NOT see how these places are "quite close together" - IMO far too much of your time will be spent in transit and unpacking/packing/checking as you zoom from one overtouristed super-high-name-recognition destination to another, and you'll be shelling out a lot of € for too little feet-on-the-ground time and contact with everyday Germany.
I would instead suggest a more direct route between Prague through northern Bavaria and then on to the Frankfurt/Rhine area. PRAGUE - NUREMBERG/ROTHENBURG - RHINE. Trimming your travel time and expenses does NOT have to mean trimming your activities or your cultural exposure.
1.) Summer luge runs exist all over the place. There's a new one atop the Loreley cliffs on the Rhine, the LORELEY-BOB.
2.) Nazi atrocities can be thoroughly explored at the Dokumentationszentrum and you can tour the Nazi Rally grounds - right in Nuremberg. Nuremberg has the KAISERBURG castle and a fine OLD TOWN zone as well - not to mentions all sorts of beer halls. Check out the sightseeing options HERE. And Nuremberg can be navigated on foot.
3.) Day trips from Nuremberg are exceptionally easy. Take your choice. Visit the Residenz Palace in Würzburg (something you might also do on the way to the Rhine.) Day trip to Rothenburg. Day trip to Bamberg. Day trip to the amazing Franconian Freilandmuseum, a collection of 400-600-year-old buildings from rural northern Bavaria. Cheap daypasses (€17.50/day for your family) get you everywhere.
A trip like this would mean only TWO major travel legs that could be accomplished inexpensively through pre-purchase of point to point tickets and/or by daypass on the regional trains. Yet you'd have your hands absolutely full of possible activities.
