We want to spend some time in a nice town like Rothenburg and some
time in Bavaria. Want to spend some time in Berlin. Is Nuremberg the
number 1 place to see for WW2 history?
The others are right about your limited time. Berlin takes 4-5 days for most, so I suggest you skip it this time and split your week+ between the Rhine/Mosel region and the Nuremberg area (northern Bavaria.) Both areas make transit to/from FRA airport easy. Both areas have several "nice towns like Rothenburg", including Rothenburg itself, which, though nice, is a sardine can for packing in summer tourists. The Remagen Bridge Peace Museum is a good WW II destination, and Nuremberg itself is good as well.
There's no problem doing this by train - just locate accommodations near the train stations in two separate base towns, one in each area. Trains run up and down both river banks along the Rhine, and the Nuremberg area is a spider web of train tracks going everywhere.
To see the Rhine AND some of the Mosel River (Cochem and Burg Eltz castle for example) the towns of Boppard or St. Goar make for good bases for train travelers.
For the Nuremberg area, Nuremberg itself is quite good; consider it first since it's the sort of place where 1 day on a day trip from somewhere else just won't cut it.
Bavarian towns you can visit from Nuremberg: Rothenburg, Bamberg, Bayreuth, Regensburg, Iphofen, Bad Windsheim, Würzburg, and others... do some research to prioritize which day trips you will make.
From a Boppard or St. Goar base: day trip to Remagen, Bacharach, Oberwesel, Braubach (Marksburg Castle), Burg Eltz*, and Cochem; some of these can be combined into single-day outings.
*(Burg Eltz requires a train ride to Moselkern and then a walk through the woods or possibly a bus ride if it's a weekend.)
Try to get rooms or apartments within easy walking distance of the station. Boppard and St. Goar are small enough that most rooms already are. Nuremberg has lots of places near the station as well.
Rhine Cruise: Most people confuse this excellent sightseeing excursion with transportation. But it's not very good transportation for hopping off and on because of the limited boat schedules. You can do it most easily in one of two ways...
a.) On your way from FRA to Boppard (or St. Goar) get off the train with your bags in Bingen, and cruise from there to your destination.
b.) Once you've parked yourselves in Boppard (or St. Goar) take the train south to Bingen and cruise back to your home base.
It's best to cruise from Bingen north rather than southbound because of the strong river current (which makes a Boppard-Bingen cruise 1.7 hours longer than it needs to be.)