OK, so with your personal interest in Bad Reichenhall, I feel really bad for suggesting you skip this area.
"Two nights Munich." Check.
"Two nights Bad Reichenhall - day trips to Salzburg and Berchtesgaden National Park."
Suggest 4-5 nights instead. (I would drop the GaPa area and Fuessen.)
Also visit the Salzburg Open-Air Museum, right near Bad Reichenhall! Great for kids and families:
https://www.freilichtmuseum.com/en/visitors-information.html
And Hohenwerfen Castle/Fortress just outside Salzburg... with a cool falconry show as well.
https://www.burg-hohenwerfen.at/en/your-visit/opening-hours
And do the Hochlenzer summer bobsled (there are a couple of other bobsled runs in the area as well.)
https://hochlenzer.de/rodelbahn.html
The Jennerbahn lift near Berchtesgaden and the Koenigssee is a thrilling experience as well. And the Berchtesgaden Salt Mine tour can be fun too.
PALACES: On your way to this area from Munich - or as you are leaving it - you will probably be driving right past The Chiemsee, also nicknamed the "Bavarian Ocean" where Herrenchiemsee Palace (another King Ludwig Palace, mentioned already by others) is situated on an island in the middle of the lake. A ferry gets you across.
https://www.herrenchiemsee.de/englisch/tourist/index.htm
That's half your trip. As for the rest... I read this...
With kids in mind, I would definitely tend to Black Forest over
Mosel/Rhine (they have a bit of a reputation for being more
interesting to older travelers).
Yes, older travelers frequent the area - BUT... the area is no old-folks home! both Rhine and Mosel have excellent medieval castle tours. For an outdoor family like yours, both offer excellent hiking trails with wonderful views that range from simple walks to rigorous climbs. Oberwesel has a fun walk along the remaining fortifications and towers of the town's old defensive wall.
https://www.tripadvisor.com/Attraction_Review-g198501-d2189241-Reviews-City_Fortifications-Oberwesel_Rhineland_Palatinate.html
https://www.niederrheinscout.com/wp-content/uploads/2020/08/Stadtmauerrundgang-Oberwesel.jpg
Both rivers have fun boat rides and cable car rides. Just outside COCHEM is this small amusement/wildlife park - with a falconry show - designed for younger kids:
https://www.tripadvisor.com/Attraction_Review-g1053688-d1905592-Reviews-Wild_Freizeitpark-Klotten_Rhineland_Palatinate.html
Cochem's indoor water park / pool facility is great too:
https://cochem.de/galerie/leisure-centre-cochem/?lang=en
https://i.pinimg.com/736x/5d/b2/e1/5db2e1bd71e0697d59996868bd3565de.jpg
Thrills? The Geierlay suspension bridge might be your thing.
https://www.geierlay.de/en/
Or just take the chairlift ride in Boppard, exhilarating at a minimum:
https://fewoboppard.de/wp-content/uploads/2015/05/Sessellift.jpg
And because of the area's nice collection of old-world towns like Bacharach - and BRAUBACH as well (home of Marksburg Castle) - I don't think you'd be missing out on much of anything at all by keeping the Rhine/Mosel and dropping the Black Forest. Braubach, 3 pages of photos:
https://stadtbild-deutschland.org/forum/index.php?thread/7322-braubach-am-rhein-und-marksburg-galerie/