Day trip from Kaub/Middle Rhine River

Also, will we run into any problems with a Sunday day trip and stores being closed? Not unless you need to go shopping for groceries or clothes. Petrol stations, restaurants and most tourist attractions remain open.

Here's just a few ideas. The walled wine town of Ahrweiler is just off the Rhine. Very similar to Rothenburg, but without all the tour buses and souvenir shops. You could also combine it with a visit to the abbey of Maria Lach.

On a clear Sunday in spring, Wiesbaden is particularly attractive, especially it's parks.

Darmstadt isn't the most immediately appealing city, but the center of the city contains some wonderful relics from it's time as the royal capital of the Grand Duchy of Hessen. And if you have an interest in Jugenstil art and architecture, the artists' colony beckons.

Consider a visit to Heidelberg and some of the surrounding wine towns, such as Wienheim and Heppenheim.

March when?
What about a totally different kind of museum?
I visited this open-air museum in Bad Sobernheim recently. Bad Sobernheim lies in the Nahe River Valley upstream from Bingen (where it empties into the Rhine.) The historical buildings here, previously scattered around the region in different towns, were dismantled, transported, and reconstructed on site. I found it truly fascinating. It opens Sunday March 19 this season.

Here's a map of the Nahe River Valley. You could make a full day of it by visiting Idar-Oberstein (mecca for gemologists and known for its cliffside church) and the old-world town of Kirn. Bad Kreuznach is charming too - check out the Brückenhäuser. The Draisinentour in Staudernheim opens the 25th.

When in March? This is a list of events happening in the Rhine Main region in March.
* 10-13 Mar. Barbarossa Market, Gelnhausen
* 11 Mar. Organ Matinee, Frankfurt Kaiserdom, 12:30 - free
* 11-12 Mar. Easter Market, Eberbach Monastery
* 18-19 Mar. Easter Market, Frankfurt Dominikaner Cloister
* 24 Mar. Organ Concert, Frankfurt Kaiserdom, 20:00
* 25 Mar. SaTOURday, Frankfurt free museum day
* 25-26 Mar. Easter Market, Michelstadt
* 26 Mar. World of Cider, Frankfurt Palmengarten
* 31 Mar. -2 Apr. Easter Markt, Wiesbaden

We are looking at Sunday, March 12, 2017.

Head over to the Easter market in Eberbach Monastery then. This is a unique market and the monastery is very old and special. I will be there on the 12th too as I go every year.
The nearby town of Eltville on the Rhine is worth a visit too. Great promenade on the river, lots of half-timbered buildings, an ancient church, and lots of wine venues. Have lunch or dinner at the Gelbe Haus.
http://kloster-eberbach.de/en/monastery
http://www.weinstube-gelbeshaus.de/index_en.html

Just make sure you note that Kaub is on the right bank of the Rhein, whereas Bacharach and Koblenz are on the left bank. There us a bridge at Koblenz, but only a few ferries up river from there. Make sure you know where you can cross the river.

RE: ferries.

As Lee notes, there are no bridges spanning the Rhine between Wiesbaden and Koblenz. I don't know the location of all the ferries, but there's at least one that crosses between Rüdesheim and Bingen and another right by Burg Pfalzgrafstein (the well known castle in the middle of the river). For a rough estimate, the drive time between Rüdesheim and Koblenz along the right bank of the river is about an hour. Traffic is usually a little heavier on the left bank and the road goes through more towns, so the drive time is a usually longer between Bingen and Koblenz.

I don't know the location of all the ferries

A list of all Rhine ferries can be found here: https://de.wikipedia.org/wiki/Liste_der_Rheinf%C3%A4hren (in German, scroll down to the "Mittelrhein" section).

Easy day trips from Kaub:

Mainz (1 hr.)
Limburg (1 hr.)
Linz am Rhein and Remagen (sights and places to eat on a walk around the town. Note WW II museum @ #18; 1.5 hrs from Kaub, opposite each other on the Rhine; use auto ferry.)