And I just looked and see that you are Hilton Diamond. My suggestion then:

from PRG take AE to Masarykovo Nadrazi and walk across the street to stay at the Hilton Prague Old Town for a night. They treat Diamonds well. (There other Hilton Prague is close by but not quite as convenient, imho.)

After breakfast, walk 10 minutes to Prague UAN Florence and catch the Flixbus to Dresden. in Dresden, walk 20 minutes or take a tram three stops and stay the night at Hilton Dresden. Last time there, I got a beautiful corner room with a view of the river and main restaurant street. Time before that I had a view of Frauenkirche.

Again, after breakfast, head back to the main bahnhof and catch the bus 2 1/2 hours to Berlin, choosing the station closest to your hotel. If you go to Alexanderplatz, you can take the U bahn 5 stops to Stadtmitte and stay at the Berlin Hilton. Go to Berlin ZOB in Charlottenburg if you are staying at the Hampton. I highly recommend the Hilton as it is an easy walk to many attractions from Brandenberg Tor to Berlin Cathedral to Reichstag to Checkpoint Charlie and more.