As far as I know, the YouTube Licensing Agreement does not allow for downloads of its content. If the content is something of your own that you uploaded to YouTube, you should be able to download a copy of your work (usually .mp4 video) from the YouTube web site in order to edit it with the video editor of your choice. That .mp4 copy should be editable in Premiere Elements 12.
Adobe Premiere Elements 12 has feature Publish+Share/Social Websites/YouTube which allows you to upload your Timeline to YouTube from that feature, not download it.
The following are links to Premiere Elements 12 specifications and supported formats.