Danny, just for comparison, here’s your two options…
Trip: Köln – Bacharach – Rothenburg – Munich / 4 days starting April 15 (sorry, it's what we've been using as a comparison) / 6 People
Option 1: Car
Itinerary: Day 1 - Leaving Köln it’s only 1 hour and 40 minutes to Bacharach. That gives you time to swing by Remagen, Koblenz, or the ever popular Burg Eltz. You’re still in Bacharach in time to explore the city, have a nice dinner, maybe take a hike.
Day 2 – With a car you’ll accomplish a lot more. Starting in Bacharach, drive down to Burg Sooneck for amazing Rhine views (not served by public transportation). Cross the Rhine and explore the 1000 year old monastery Kloster Eberbach, have a wine tasting at Schloss Johannisberg, jump up the road in 10 minutes to Rüdesheim for some touristy shopping and take the gondola above the vineyards to the Niederwald Monument. Drive up the Rhine, under the Loreley and cross at the ferry by St. Goar. Explore the old town and drive up to Burg Rheinfels before heading back down to Bacharach. That whole trip will only involve 2 hours and 30 minutes of very scenic driving, which gives you the rest of the day to explore two castles, a monetary, a vineyard, several small villages, and take gondola ride.
Day 3 – The drive from Bacharach to Rothenburg only takes 2 hours and 30 minutes. You’ll arrive in Rothenburg by lunch which gives you the rest of the day to explore the city.
Day 4 – The drive from Rothenburg to Munich Hauptbahnhof is also only 2 hours and 30 minutes. You’ve just spend a day on the Rhine and a day in Rothenburg so I’m guessing everyone has had their fill of old German towns. Get to Munich before lunch, drop off the car, and enjoy a long lunch in
Total driving time (not including the day driving around the Rhine): 6 hours 40 minutes
Cost: I shopped around and found a VW Sharan on Avis for €329. Holds 7 people, includes liability coverage, pick up and drop off at the train stations. Per ViaMichelin gas would €120, let’s include an additional €25 for parking and side trips. Total cost: €474 - Price per person: €79
Option 2: Trains
Itinerary: Day 1 – Leaving Köln it will take you anywhere from 1 hour 40 minutes to 2 hours 30 minutes to take the train to Bacharach. Spend the rest of the day exploring Bacharach.
Day 2 – Spend the day exploring the Rhine by linking together public transportation options provided by both the ship and trains. Allow additional time to wait for buses and trains to get you around.
Day 3 – It’s a 4 hour and 20 minute train ride from Bacharach to Rothenburg with three transfers. If you leave at 8:30 am, you’ll be there by 1pm. Spend the rest of the day exploring the city.
Day 4 – It’s a 3 hour and 15 minute train ride from Rothenburg to Munich with two tight connections (4 minutes each). If you leave at 9am you’ll be in Munich by 12:21.
Total train travel time (not including the day spent exploring the Rhine): 9 hours 15 minutes
Cost: Train to Bacharach €70, KD cruise tickets €88, Train day pass €50 (I’m not sure what you would buy, but usually passes only cover up to 5 people, so you would need to buy two passes), Train tickets from Bacharach to Rothenburg €239, Train tickets from Rothenburg to Munich €115. Total cost: €562 - Price per person: €93 / You could not do the KD boat ride (as my car trip suggestion didn’t include it) and the price would drop to €474 or €79 per person – exactly the same price of taking a car.
For the above prices and times I tried to get the cheapest prices and the best travel times at bahn.de. To be fair, someone may know of some Länder-Tickets that I’m not including that would drop the cost a bit, but I believe this would only add to your total travel time, which is already approaching 10 hours.