I tend to let people do as they wish, and I have done trips like this earlier in my travels, so if the pace works for you great. But, through experience, I have found that you need to have realistic expectations as to what you can accomplish in the time you allow. If you are satisfied seeing only a portion of what an area offers, or passing through and getting an overview, or just to see that one thing you wanted to see, then you are on the right track. In regards to that, I can though make a few suggestions.
Travel from Rothenberg and two nights in Bacharach does not allow enough time for a boat ride (easily half day activity) a visit to the Mosel valley (another half day minimum from Bacharach, more like a full day), and both Wurzburg and Frankfurt, I presume as stops between as you travel. You can certainly get off the train and take a look around, but you might want to lay out what you want to see in each place, and figure out some timing. Many love Frankfurt, but getting off at the main station and wandering the surrounding streets is a bit dreary, likely you will be taking public transport to what you want to see. Wurzburg, you could certainly stash your bags, wander through the old town, maybe have a glass of local wine, but visiting the Residenz palace and cathedrals starts to consume hours on what is a 4-5 hour travel day already.
Having a car after Frankfurt until Cologne might make it more efficient to explore. Again, not sure what all you want to see, but the high points in Cologne can be done in an afternoon (the Cathedral and wandering old town), giving you a bit more time to drive the Mosel.
For Belgium, you might reconsider the order. From Cologne Brussels is a good first stop, then Bruges, then Antwerp. Many do not realize that the Brussels airport is almost as close to Antwerp in travel time as is where you will stay in Brussels. In Antwerp there are great hotels near the train station, not so much in Brussels. For that matter (again, depending what you want to see) you could stay your two nights in Ghent, and day trip to Brussels, or spend mid-Day in Brussels enroute Cologne-Ghent.
