I took the bike over to Berlin last May. I used the tunnel (partly for curiosity as I'd never been on it before, and partly for speed - an impressive 25 mins) to cross the Channel. My main intention was to see some of the World War II sites, eg Eindhoven, Nijmegen, Arnhem, the Airbourne Museum in Oosterbeek etc. I guess your wife may not be overly keen on the military history, so why not take the ferry to Amsterdam.
Link to Eurotunnel prices etc
HERE
It took me 2 days to get to Berlin itself. The first day was spent in France, Belgium and the Netherlands. I ended the first day in a town called Bad Bentheim just over the German border. The second day I spent travelling along the Autobahn directly to Berlin (with an approx 90 mile round trip detour to visit Bergen Belsen). If I'd gone directly, it would have taken approx 5 hours riding time. Using the Autobahns mean you can cover big distances in a shortish time, but a word of advice -
be very careful when changing to their equivalent of Lane 3. Although I didn't see an accident, I saw several "near misses" and the speeds some of the cars travel at don't give a big margin of error. You could be cruising along quite happily in Lane 3 one second and literally within 10 seconds, you would see a pair of headlights in your mirror approaching at speed.
I would definately recommend GPS. I took a paper map as a back up but I don't think I looked at it once. In your case (with 2 of you) guiding by map would be easier, but the GPS made the trip a joy.
I also found the GPS superb for finding places to stay, but the only hotel I booked before leaving was the
Ibis Hotel in Berlin. The secure underground car park was the best I have used, and was worth paying a bit extra for the peace of mind that the bike was safe. If you need the tel no, address etc PM me. Somehow sorting out the accommodation while on the road, added to the adventure.
I only spent 2 days in Berlin - which wasn't enough. If I find myself in that area again, I would definately go back for a second visit. I'm sure you will love it.