A DK2 asks a lot of your GPU compared to a monitor.
Did you try to lower your quality settings?
You should be able to isolate the core of your problem by doing some research and profiling as described in the tutorials.
When I had the same problem with a DK2, the “stat unit” command in the console showed me that my GPU was the weakest link. After profiling as described in the tutorials, I found out that the GPU spend too much time on unnecessary complex lighting. The framerate improved by 50% when I replaced that part.
A fast way to increase the framerate (while loosing quality), try the console command: hmd sp 100 or hmd sp 70