Klewalle: "...then daytripping to Neuschwanstein the 26 and then taking the train to Cologne that evening."
No matter which day you travel, and even starting out from Munich's main station, the public transport alone (trains + buses) to N'stein and back will require nearly 5 hours. Then in Munich you would fetch your bags and take the train to Cologne, a minimum of 4.5 hours (and that's using the fastest possible route, which bypasses the Middle Rhine Valley.) None of that time includes the time you'll spend on foot getting to the castle from the final bus stop or the walk back, or the actual tour time (30 minutes) or any meals along the way. There are only so many hours in a day. So you probably need a different plan. (N'stein is a late 19th-century palace with a fake castle exterior, btw.)
The 30-minute tour of N'stein IMO isn't worth the 5+ hours additional hours it will take to see it. I suggest you catch a morning train out of Munich in the direction of Cologne and see Marksburg Castle (in Braubach) instead. The 1-hour tour of a genuine, never-destroyed medieval castle, set in the scenic Middle Rhine Valley, is very good and is doable on the way to Cologne. Marksburg is open 11-4. The 7:27 or 8:52 trains out of Munich will get you to Koblenz in less than 5 hours. You can stow your bags in a locker there and take the 10-minute train ride to Braubach for the castle - then return to Koblenz, fetch bags and head to Cologne. Have a meal in Braubach or in Koblenz. The Zum Goldenen Schlüssel in Braubach's attractive old town center serves good, traditional German food.
You can find all the possible train connections for any day of the year at the DB itinerary search page: http://reiseauskunft.bahn.de/bin/query.exe/en
Personally, I would make it even easier on myself than I just suggested. Make the train trip to Koblenz and check in there for the night. Then do the castle trip and return to Koblenz. Travel to Cologne the next morning.
Visiting Marksburg (like Neuschwanstein or any castle you have to walk up to) will depend to some extent on weather conditions.
Whether you visit Marksburg or not, it is probably a good idea to route yourselves to Cologne along the Middle Rhine Valley to catch a glimpse of the 40 castles that dot the cliffsides between Bingen and Koblenz. To ensure that you get a travel schedule for the trains along this route, enter a stopover in Koblenz at the DB site with 00:00 stopover time. That will get you routed through the MRV on the way to Cologne.