Lucerne Switzerland vs. Rothenburg Germany

Just my opinion, but as quaint as Rothenburg is, its not worth going that far out of your way to see. Lindau on the Bodensee is scenic and quaint (and flat), and closer to Zurich. Appenzell region in Switzerland should have some options to consider.

Hands-down Lucerne. Rothenburg is nice but it's quite small.
Lucerne has a lot more to do and see and, with your husband's mobility issues, riding around the lake on a boat would be a really nice thing to do. There are several nice little villages around the lake. You can also ride the gondola up to Mt. Pilatus...stunning views with no hiking!
You can easily spend2- 3 days in the area of Lucerne and not run out of things to do.

We liked both towns, but Lucerne and the lake would be my pick. Another option would be to stay on the Wolfgangsee in the Salzkammergut by Salzburg for your Salzburg visit and add a day/night there to give you a chance to explore the other towns by lake ship.

Paul

You should consider going to the picturesque villages near Colmar, France (Riquewhir, Ribeauville, etc.) which are small, medieval like towns like Rothenburg and not very far from Switzerland. Although these villages are in France, this is the Alsace area of France that has a lot of German influence and similarities (such as the Fachwerkhäuser buildings) and use to dealing with German speaking visitors.

Lucerne or Rothenburg? Lucerne. It's closer to the places you plan to visit and also it has a very beautiful scenery.