If the Rift as secondary, vorpX to “Show on DK2” method does not work for you (normally it should for Skyrim and most other games), you have to resort to DK2 as primary, vorpX to “Use system settings”.
That is pretty inconvenient for sure, but not impossible. You can either try looking through the Rift’s lenses with one eye, and use the desktop this way, or rearrange your whole desktop including moving the taskbar back to your monitor as a more permanent solution.
Direct to HMD is not supported currently. It may work with some games (including Skyrim), but Direct to HMD directly conflicts with what vorpX does, so this is not officially supported at all currently.
The two “official” setup options are described in the DK2 Setup Guide in the documentation.
Please also check your Skyrim folder for a d3d9.dll and remove it if you find one. In case you use many mods, try a fresh install without any mods.