Amsterdam, then Germany in the fall

We haven’t figured out all the things we will do at each location yet,

For my way of thinking, that's a problem. What I want to see/do comes first, how to get between the sights/activities second; where I spend my semi-conscious hours is WAY down the list, somewhere next to my restroom stops.

For example... Fall means harvest and wine festivals. During your time, I'd want to hit one of those. The town of Boppard has one across two weeks in late September and early October. I'd want to book a couple of nights there at a minimum, probably more nights to see some of the awesome stuff around there. If my hotel is in COLOGNE, I would not want to be daytripping there and back constantly.

https://www.boppard-tourismus.de/en/news-events/whats-on-throughout-the-year/

https://www.mosel-inside.de/en/travel-guide/mosel-villages.html
https://historiceuropeancastles.com/the-best-rhine-river-castles/

Consider taking the train from Cologne to Wurzburg. You'll probably have to change trains in Frankfurt, but at least you'll not have the hassle of driving in Frankfurt. In Wurzburg you can visit the Prince Bishop's Residenze,
and several othet attractions, and then rent the car for the drive to Rothenburg. Of course you could take the train from W'burg to R'burg.

Be aware that October 3 is Germany's national holiday and lots of things will be closed.