Our recommendation for you is to keep using the Web-Based SlingPlayer, since having the full screen using dual monitors is a feature of the SlingPlayer 2.0 and it is not possible to disable it, since it is no longer developed.
I had exactly the same problem and even posted a question on this forum attempting to get it corrected (which I figured out on my own). In the end, I was able to find a setting in my video driver software that corrected the issue. I am using an older Dell Laptop with an NVidia video card. Within the NVidia Control Panel software I found a "Video & Television" section that has an area to "modify full screen video options". Change the selection from "Autodetect" (which was displaying the Sling video on both screens to "Only show it in my viewing application". This corrected the issue for me on both the desktop and web Sling viewers.
I am currently set with a large, external monitor as the primary display when docked and the laptop display as the secondary. I run Sling desktop viewer in full screen on the laptop display and do the my work on the external.
If you don't have an NVidia card, you may have a similar setting in your card's software.