Help: one night stay on Rhine between Amsterdam and Nuremberg

My choice would be Boppard, because it has the best selection of hotels and restaurants on the Middle Rhine. There is also a multi-storey car park in the centre and two parks decks on the southern edge of the old town.

have avoided long car trips as much as possible

Nevertheless, I'm afraid that's what you're planning. Because even if the two legs between Amsterdam and Nuremberg are only just under 400 kilometres, they still lead along motorways which are among the busiest in Europe and guarantee a stressful journey.

I would prefer to travel by train. And if your stop after Munich ("Mosthause"??) should be difficult to reach by train you could always hire a car in Munich or Freilassing, depending of its exact location (we can't say more precisely because afaik there is no place called "Mosthause" in Bavaria or Austria).

Boppard ...here Hotel Bellevue
almost half the way Amsterdam Nuremberg Exit 41 on Autobahn 61 from the north

The Bellevue would also be my recommendation, but they usually accept single overnight stays only in the low or shoulder seasons (cannot hurt to try it on the hotel's own booking platform - greater chance than on booking etc.). There are a few other hotels in the neighbourhood, e.g. the Baudobriga, Krone, Günter, Ebertor. I only know the first one, which of course can't compete with the Bellevue, but also costs much less and was completely ok overall.

Sounds like you're planning on 4-5-hr. minimum driving days for A'dam > Rhine > Nuremberg. Normally, Boppard is my go-to suggestion too, but you are staying only one night, and with so little time for the area, it does not sound like you are planning to do a Rhine cruise, or tour Marksburg Castle, or travel up the Mosel to Cochem or Burg Eltz, or wander around Bacharach, or do any hiking, all the sorts of activities that make Boppard such a great base town. Your only criteria seem to be "small" and "picturesque," which means other towns might work just as well in your case.

The other factor is your timing. The Middle Rhine Valley is having one of its biggest weekends from Sep 12-16, the Oberwesel Wine Market festival, and ALL the left-bank Rhine towns will be heavily impacted, with crowds, traffic, and overbooked hotels the entire time. Saturday will be the biggest day of all. In Oberwesel, Bacharach, St Goar, Bingen, and Boppard, whatever your hotel criteria might be, you might be lucky to find anything at all, much less what you are looking for in a hotel (which I assume is a room with a nice view, maybe air conditioning, at a minimum.)

So you will need to keep your option wide open, I think. Perhaps the right-bank towns will be a little less busy. I have stayed in tiny Osterspai previously - a quite, lovely quiet town just upstream from Braubach and just across the river and north of Boppard.

https://www.youtube.com/watch?v=V4E5FyzrK98
https://osterspai.welterbe-mittelrheintal.de/urlaub-und-uebernachten/gastgeber

Braubach itself, just a few minutes from Koblenz, is also small, with a lovely old town zone and a few places to find dinner. Scroll through these 3 pages of photos to get an idea:

https://www.stadtbild-deutschland.org/forum/index.php?thread/7322-braubach-am-rhein-und-marksburg-galerie/
https://www.tripadvisor.com/Hotels-g642094-Braubach_Rhineland_Palatinate-Hotels.html

Or perhaps you will find something that suits you on the nearby Mosel River, or in the Lahn or Nahe River Valleys.

Wow, lots of driving. Starting in a rail hub like Amsterdam, have you considered trains? There is a direct ICE train to Cologne. You could then pick up your rental or take another train to Koblenz. Granted, I don't think Koblenz is the quaint Rhine town you're looking for.

If you stuck with trains until Munich, Koblenz would be a good Rhine base as it also has a direct connection to Nuremburg, which has a direct connection to Munich.

I don't know what "Mosthause" is.

Try Eltville. For me, one of the prettiest towns on the Rhein. Has lovely hotels and great restaurants, and a lovely promenade walk along the Rhein. The dry moat from the former castle is filled with 100s of rose bushes. A visit to their ancient church would be nice too.

I’d stay in Bacharach. The Im Malerwinkel ( painter’s corner ) is in a great pretty area and has excellent parking

As noted the Rhine is already booked and will be jammed. You're looking at 5-6 hours driving (minimum) on some of the most under construction roads in Europe. If you must, don't go into the Rhine valley for lodging (it's probably too late anyways). Stay in Koblenz. There you have a great city, huge history, the Eck, Ehrenbreitstein, and walks along the river with good lodging and food.

But then you face another 5+ hours to Nuremberg, which is fantastic. Do yourselves a favor and fly to Nuremberg. Seriously.

For a scenic route between the Rhine and Nuremberg ..go away from the Rhine at Bingen. Cut across to Bensheim. Then thru the Odinwald via Michelstadt, Amorbach, and Miltenberg to the Main River. Continue to Wertheim. Then it will probably time to get on #3 and take it to Nuremberg