We have 11 days to spend in Alsace and Burgundy flying in and out of Zurich (although Frankfurt could be an option. We intend to rent a car.

We are currently booked just outside Kaysersberg for 3 nights, near Mulhouse (Hochstatt) for 2 nights, Beune for 4 nights. We leave Beaune early Friday Sept 22 and fly from Zurich late afternoon Sept 23.

1. Would you stay all five nights in Kaysersberg area and cancel the Mulhouse accommodation. We intend to visit the towns along the wine route and Strasbourg/Colmar. We are unfamiliar with the Mulhouse area.

2. Where would you overnight en route from Beaune to Zurich knowing our flight is 5:30pm the following day? Our thoughts were Lucerne or closeby.

Any other suggestions would be greatly appreciated.

Lucerne if you've never been there for sure! Not a bad town to drive in-Bern would be nice but it is larger and not so gorgeous as is Lucerne on its lovely lake. Lucerne to me.

Strasbourg IMO deserves at least a whole day - do Colmar on another day.

If you drive from Beaune via Salines royales d'Arc et Senans - Pontarlier - Val de Travers - Neuchâtel (castle, lake) - Lake Biel vineyards - Solothurn (baroque city) to Zurich, you may have no time for Lucerne.

I don't see any reason to move to Mulhouse for a couple nights en route. It's not that far from Colmar anyway, and the entire drive from Colmar to Beaune also isn't that long, so it's not like you need to. If you wanted to spend some time in a city, I could understand it (although I would probably pick Besancon, not Mulhouse), but not just to stay in a suburb of Mulhouse.

That's mainly an industrial area.

Mulhouse has fine automobile and textile museums and the Ecomusée d'Alsace (open air village museum) isn't far away. Close to Belfort-Montbéliard, you may visit the famous church of Ronchamps (Le Corbusier) and/or the Reclere Caves (stalagmites/stalagtites and Dinosaur Park).
Besancon has a medieval fortress as well as art and watch museums.