It sounds like you are hitting the wrong element in MyComputer if the Twonky UI is popping up; the MyCloud appears as three entities in MyComputer; the file server, the Dashboard UI and the Twonky UI. For file operations, you need to access the file server.
I’d strongly advise you to download and read the user manual. In particular, read about how to map Shares as network drives; then you can access the drive like any other named drive on your PC.
The MyCloud is not a ‘hermetic environment’; it can be integrated seamlessly into Windows file system, and needs no WD software to access it locally. For remote access, again, it would be instructive to read the user manual to learn how to set up the MyCloud, and access it remotely. Having bought a second device, it took me about ten minutes to have it set up, from first applying power.
