Your 2nd post helps clarify things.
April - May: a fine time for smaller places and being outdoors (I figured December when you mentioned "Christmas shops" but I suppose some indeed are open in tourist-towns.)
Spellings were provided NOT to achieve an apology! Only to help you avoid troubles if you need to buy tickets to those towns or research them further.
I'm open to any recommendation of ways to get to/from Krakow...or to
knock it from the itinerary by replacing important concentration camp
sites in Germany.
If your sole purpose in Krakow is really Auschwitz, I'd say drop it. Dachau KZ camp is about 30 minutes from Munich. Sachsenhausen KZ camp is an easy day trip from Berlin. It's almost inconceivable to me that more than 1 or 2 concentration camps would be on anyone's itinerary. And Krakow/Auschwitz would indeed be a lengthy detour.
Hubby and boys are very interested in WW2 history.
Easy to find museums and historical sites when you research Berlin and Munich. On the Rhine there's a lesser known WW II museum in Remagen where the "Bridge at Remagen" once stood. Very worthwhile:
http://www.bruecke-remagen.de/index_en.htm
Remagen - interesting town in a scenic spot: https://www.remagen.de/Tourismus-_-Veranstaltungen/Stadtrundgang/
I am homeschooling my children, covering World History...
The Mosel River town of Trier is very good place for learning more about Ancient Rome in northern Europe.
https://www.trier-info.de/english/unesco-world-heritage-sites
https://www.trier-info.de/english/sights-in-trier
Outside Trier:
If you can be there on a Sunday afternoon, visit this former German military installation on the Westwall.
Bernkastel (also on the Mosel) has one of Germany's most stunning collection of old half-timbered buildings (does get lots of weekend tourists however.)
Lots of Middle Ages history on the Rhine at castles like Marksburg, at Rheinfels and at Burg Eltz.
About half way between the Middle Rhine Valley and Stuttgart, Ludwigsburg might be a really good place to explore a completely different historical period.
And half way between the Middle Rhine and Ludwigsburg is Speyer, home to an outstanding technology museum that runs down the history of submarines, space shuttles and more. Speyer has one of Europe's most outstanding Romanesque cathedrals as well.
Surely we must visit Berlin, Munich, and Salzburg..but I'd love to
base ourselves outside of any cities.
Outside Salzburg you might consider Golling (small town on the Salzach River.) Guests get a free "Tennengau Card" for free train transport into Salzburg (where parking can be difficult.) It's also valid on certain bus routes to smaller mountain towns. Note that this flyer is dated - the card used to cost €4 but is now free: https://www.golling.info/images/TennengauPlus/Folder_Tennengau_Ticket_DE.pdf
We were just in Golling and took a day trip to nearby Werfen (Hohenwerfen Castle and falconry exhibition; Eisreisenwelt ice cave; Sound of Music Trail. Other outings are possible too.
I would base within Berlin to save time - 5 days?