Hi,
It would be better time wise if you had 3 weeks to do this itinerary. From Düsseldorf to Mainz each of those cities Wuppertal, Köln, etc is just a morning ride. Leave at 0900 or so at the latest you'll be in the next city prior to 11 am or at noon, even better if staying near the train station. What time are you landing in Berlin?
I did the morning train Berlin to Düsseldorf last June, got in ca 1400 or so. I would assume the earliest you'll get to Düsseldorf would be between 1600 and 1700hrs. Take the ICE direct Berlin Hbf to Düsseldorf Hbf. That's doable. The one city on your itinerary I never got around to visiting is Wuppertal, even through the train often stopped there.
Still even with a two week constraint, the trip is a bit rushed, but doable! The afternoon in Koblenz I would suggest seeing Deutsches Eck where the Mosel and Rhine meet. To get a good aerial view of that, go to Ehrenbreitstein, used to be Festung Ehrenbreitstein, the big Prussian fortess built after Napoleon's defeat to protect the Prussian Rhineland area and to guard against a resurgent France. Ehrenbreitstein is now the HI hostel, stayed there too.
I would suggest staying at the train station area, no need to rely on public transportation or worse still a taxi on departure day to reach the train station, just walk the 2-4 mins. The itinerary is good , I can think of places to visit in each of these cities but that also depends upon your interests unless you're open to cutting a few places. You can choose between Bonn, Bad Godesberg, Bad Ems, Ingolstadt, Weimar.