"Our original plan was to spend four or five nights in Stuttgart, (with a daytrip to Triberg and Gengenbach),"
"Would it make more sense to make Stuttgart and Bavaria our main focus - maybe do a daytrip over to the Rhine, or possibly spend four nights in both and three in a place like Dusseldorf?"
Stuttgart as a base: I think you'll find an outing to the Middle Rhine Valley (the Rhine everyone wants to see) a very impractical day trip from D'dorf, Stuttgart or "Bavaria." Practical day trips from Stuttgart might include Ludwigsburg, Tübingen, Esslingen, Bad Wimpfen on the Neckar River or maybe Calw (less than 1 hour from Stuttgart) in the northern Black Forest. These are all really nice places. Gengenbach is very nice - but that will involve 5 hours of driving round trip from Stuttgart (assuming you're driving.) Triberg is less impressive and just as far.
If you go to Stuttgart, be sure you have specific sightseeing goals in mind and figure out how to get there. It's not high on my list of places to just hang out but it does have some worthwhile sights. If you're doing multiple day trips, I would actually prefer to stay in a place like Tübingen and day trip into Stuttgart (probably by train) rather than have to drive out of and back into Stuttgart all the time.
The Rhine: If your disability involves walking, there is parking at both Marksburg and Rheinfels castles. It's a 5-minute walk to Marksburg from the lot. There are shuttles up to these castles from town but not in the fall. The castles themselves involve some up and down, however. I would suggest a visit to the Mosel River town of Cochem and the castle there. A shuttle bus runs to the castle from town in the fall as well, and once you're up there, you don't have to tour the castle (which also involves steps) but you could easily enough take in the excellent outdoor falconry show and enjoy some refreshements from a seat on the terrace that overlooks the town and river valley:
View from the Burgschänke at Reichsburg
Falconry show photos (shows at 11, 1:00, 2:30, 4:00 daily except Mon.
There's also a chairlift ride in Cochem that's easy to reach on foot but takes you high above town for a view.
I would not skip the Rhine towns. Boppard (also has a chairlift,) Oberwesel and Bacharach are all south of Koblenz and small, relatively flat (for easy walking,) special towns you probably want to see. Linz am Rhein, north of Koblenz, is too. Bingen (best place to start a river cruise to St. Goar) has a nice flat river promenade where the boats pull up with a lovely view of the river and cafes along the way:
PHOTO