Looking at your actual time for seeing/doing here...
12 days, minus Day 1 and Day 12, minus 50% of Day 2 (arrival, transfer, hotel check-in,) minus .5 days for Nuremberg > Koblenz (transport) + minus .5 days for Koblenz > A'dam (transport) = approx. 8.5 days
Your travel goals seem too demanding for this period of time to me, even if you were a group of active adults. 3 and 5-year-olds, even if they are generally "good travelers" at home, will likely require more attention and more down-time than they might if they were at home. My daughter was 9 and already well traveled back home when her first trip to Europe took place, and while thrilled to be going, she still found the travel and the cultural changes intimidating and unnerving to some degree.
Leaving out the food and beer... you are looking for... "local culture, nature/hiking... history, small dose of museums, and exploring small towns." IMO Munich and Amsterdam seem to lie outside your stated interests and are very likely too demanding for your family and the short time you have. My take is also that your itinerary appears to dedicate days 1-2 mostly for the half-hour tour of Neuschwanstein plus maybe Hohenschwangau? This day trip is roughly 5 hours of transport on a day outing. I think your kids will have plenty of time to see it on their own at some later point in life when there's more time to dedicate to the other sights in the German Alps.
Suggest this modified itinerary instead...
DAY 1: Arrive MUC, transfer to FREISING (15 minutes by train or bus.)
Freising is a small, walkable, attractive Bavarian town with good railway connections (if you need them) and a good place to get your bearings on Day 1 and settle in after an overnight (and perhaps sleepless) flight. Read below on things to do that day, food, beer, hotels:
https://www.tripadvisor.com/Tourism-g198549-Freising_Upper_Bavaria_Bavaria-Vacations.html
DAYS 2, 3: Rent a car. Drive to ROTHENBURG for 2 nights. Not my favorite place, but you want to go there, and it's a small town with some history to it. Take a day trip by car or by train on Day 3 to Bad Windsheim for the Franconian Freilandmuseum, where you really get to see and experience local history. AND it's a great spot for traditional food and beer-lovers.
https://www.tripadvisor.ca/Attraction_Review-g198421-d284746-Reviews-Frankonian_Open_Air_Museum-Bad_Windsheim_Middle_Franconia_Franconia_Bavaria.html
https://www.beerwanderers.com/freilandsmuseum-kommunbrauhaus-burgerbrau/
DAYS 4, 5, 6: Drive to BAMBERG (3 nights) stopping on the way in the small Main River old-world towns of Ochsenfurt, Sommerhausen, Marktbreit, and/or Iphofen. Tour Bamberg on Day 5; maybe drive to Staffelstein to see the incredible Vierzehnheiligen. Day 6: Day trip by train to Nuremberg for the sightseeing you planned.
DAYS 7, 8, 9: Drive to B0PPARD (3 nights), stopping in Bacharach for a look around town on the way. This is where your nature and hiking come into play (Rheinsteig / Rheinburgenweg trails.) Other options: Rhine Cruise / Marksburg Castle / outings to Rüdesheim, Oberwesel (town wall walk), St Goar (Rheinfels Castle) / "Park am Mäuseturm" in Bingen (riverside Playground/Park) / Loreleybob (summer bobsled run)
Day 10, 11: Drop car in Koblenz or Bonn; train to the Netherlands. I'd avoid A'dam personally with young kids. Not too far are other nice towns. You might enjoy the handsome old town of Naarden, near Bussum, less than 1 hour from Schiphol airport.