Germany itinerary

You could spend a week seeing each of those river valleys. But in the first week of April with Easter coming on the 12th, there will not be much activity there, and the weather may not be cooperative, so a couple of days for the highlights might be alright. Cruise boats start cruising around Good Friday, possibly a little earlier. If you stay in the town of Boppard (attractive old-world town, larger and livelier than most) you'll be well positioned for seeing a few things on both rivers. Marksburg Castle in Braubach (open year-round) ought to be near the top of your Rhine list; also look into visiting the towns of Boppard, Oberwesel, and St. Goar (home of Rheinfels Castle) on the same side of the river as Boppard. Cochem will be the liveliest of the smaller Mosel towns. All these places are accessible by train or by car.

Not sure whether Burg Eltz will be open yet; it's the best Mosel River castle option, though it's not actually on the river but tucked away up in the forest.

Welcome to forum.

You plan to have 1 full day in Berlin which is really too less for that city. Even if you do not want to visit any museum you can easily spend 2-3 days by exploring the very different parts and neighborhoods or some of the top 10 sights of the city.

The educational options in Berlin are extremely manifold.

For travel plans start with the Deutsche Bahn website for travel times/destinations/costs.

https://www.bahn.com/en/view/index.shtml#slc

Given your itinerary in westernmost Germany, Belgium and the Netherlands I am confused as to why you want to fly into Berlin which is 4-4.5 hours away from Dusseldorf. It is only about 2 hours from Brussels to Dusseldorf. So it could be US-Brussels - Brussels-US as easily.

I think that you might want to think about the "10 days" in Germany (which includes the conference times) based on what you want to do during the days, and where you want to spend the nights. You don't mention your objectives in either Belgium or the Netherlands, so it is hard to make more detailed comments on that part of the trip. The Germany part of your trip seems to focus on having half of it in day trips out of Dusseldorf (for obvious reasons), so you have already mostly answered your own question about a "central hotel." But Dusseldorf is not very central to the most scenic and most interesting (to me) parts of the Rhine and Mosel valleys, so you may need to pick one or the other. Koblenz is far more "central" to the area being at the confluence of the Rhine and Mosel Rivers.

Maybe instead:
March 26–leave from USA for Brussels.
March 27-29– Bruge Belgium, which is a great 2-3 day stop, or go straight to Dusseldorf and begin touring the Rhine/Mosel valleys immediately.
March 29–go to Düsseldorf
March 30-April 3– Conference week in Düsseldorf.

Day trips to Cologne, Koblenz and take a Rhine riverboat south from Koblenz through the Rhine Valley, catch a train back, or stay one night near Bingen (St. Goar or Bacharach) on the night of April 4–and then return to Koblenz or Dusseldorf. Maybe husband can catch a train to join you in the Rhine Valley so you don't have to go back to Dusseldorf on the last day of his conference. In particular the kids might enjoy the Marksburg Castle in Braubach on the east side of the Rhine, which is the best preserved in Germany and the headquarters of the German Castle Association.
https://www.marksburg.de/en/

April 5–Mosel valley, return to Koblenz.
April 6–leave for Amsterdam?

Visit Trier in the Mosel Valley area.

Welcome to the forum! I'm very excited that you have the opportunity to travel to Europe!

I share MarkK's sadness that you will have so little time in Berlin, but I LOVE Berlin and think a little Berlin is better than no Berlin. If you can leave the US a day earlier to squeeze in an extra day in Berlin, it would be well worth it.

My experience with Düsseldorf consists of once flying into the airport there and promptly catching a train to Dortmund. So, I don't have much to offer there. Rick Steves ignores the city in his guide book, so you have to look elsewhere (The Rough Guide to Germany? Google "What to do in Düsseldorf"?) for coverage of it.

Russ gives good advice on the Rhine/Mosel issue. Given that the Rhine/Mosel valleys may not be in full tourist mode when you are in Germany, you may also consider Aachen. It's along the train line from Düsseldorf to Brussels (less running around Germany) and contains the UNESCO World Heritage Aachen Cathedral, which was erected on the orders of Charlemagne from 796 to 798 AD and was where the Holy Roman Emperor was crowned as the King in Germany from 936 until 1531. There is a once daily English tour that lets you view the Throne of Charlemagne, a modest throne put in the cathedral by Charlemagne that was used in the crowning ceremonies mentioned earlier. Things to do in Aachen: https://www.penguinandpia.com/en/things-to-do-in-aachen/

Düsseldorf is in an area that is primarily known for mining/metal industry and if that interests you and your children at all there are plenty of historic sites and museums to visit, in particular the Ruhr Museum at the former Zollverein coal complex in Essen, and the former steelworks now converted to a public park, the Landschaftspark Nord in Duisberg.

Brühl south of Cologne has one of Germany's biggest theme parks, Phantasialand.

Another unique sight in the region is the Wupperthal Schwebebahn, a late-nineteenth century suspended monorail that is still used as an everyday means of transport. Unfortunately, it is currently out of action for renovations but may be working again by April - check online closer to the date.

From the Rhine/Mosel area to Brussels you basically have two options, either to return to Cologne and take the high-speed route from Cologne to Brussels, or to take the slower but quite scenic "classic" route via Trier and Luxembourg. The former may be faster than the latter depending on where you start from.

Good choice in going to Dortmund if you're into one of the best and well-known German beers, lot of varieties in Dortmund.

"...a little Berlin is better than no Berlin." How true!