What to do in Germany in the winter?

[chinateapot]

So.... we’re going to be spending 6 weeks in Germany in November / December near Düsseldorf. Need plans to make the best of it! What would you do with 2 adults and 2 kids (age 7 and 12), small one likely to be tired and a bit fragile. We’ll have most of each day free and every weekend. Hoping to stick to public transport mainly.

The Aquazoo and the Neanderthal museum are both great and highly interactive.
The Legoland Discovery Centre in Oberhausen is all indoors. The main station Oberhausen is accessible by the Deutsche Bahn from everywhere in Germany. Take the bus to 'SEA LIFE / Marina' (approx. 100 metres away) or to 'Neue Mitte' (approx 1 km away).
The Bottrop Alpine Centre is the longest indoor ski slope in the world and is open all year round for skiing, snowboarding and tobogganing. From Bottrop main station take Bus 262 to "Eigen Markt". At the station ZOB change to Bus 263 to "Boyer Straße / Essen". Final station is "Alpincenter."
The German Mining Museum in Bochum is good. There are special guided tours for children. Bochum main station is well connected to the German ICE and IC network. Take the subway "U 35", heading to "Riemke Markt" and exit at the "Deutsches Bergbau-Museum" station.
In the Allwetterzoo Münster (All Weather Zoo) the most important ways between the indoor areas are roofed as well. It’s a really good wet-weather day out. Münster main station is on the German IC network. At Münster main station take a bus (line 14), heading to 'Zoo' and exit at the final station.
Phänomania field experience in Essen has lots indoors. From Essen mainstation use the tram 107 to Gelsenkirchen Hbf. Change at the station 'Abzweig Katernberg' to the bus 348 to Gelsenkirchen and get off at 'Huestraße'. There you will see phaenomania.
Take the train to Cologne for the day and visit the chocolate museum. The Cologne main train station is reachable from all directions with Deutsche Bahn trains. From there the Chocolate Museum is accessible with the bus line 133 to Schokoladenmuseum. Alternatively the "Chocolate Express" (Bimmelbahn: Schokoexpress) runs daily every 30 minutes from Cologne Cathedral through the old town to the chocolate museum.

Thank you so much, this is exactly the sort of thing I need x

As you'll be there in December I'd enjoy the Christmas markets. They're much, much nicer than the Christmas markets in the UK. I would avoid the big city ones and instead go to the smaller ones as they're less busy and will be easier for your seven year old.
I'm sure you'll do this, but take a good warm coat and decent gloves/ hat /scarf. I lived in Germany for three years and December can be very cold (though not as cold as January, and I was further east than you'll be). If your children feel the cold I'd also buy a pair of silk socks for them to wear under normal socks / boots etc as they're a great way to stop feet freezing!
If you decide to go away for a weekend then the Eiffel hills, the Harz mountains and the Rhine valley near the Lorelei are all very scenic.
Germany is great, I hope you have a lovely time.