It sounds like a download rather than an upload from YouTube that you are asking about. Please read on.
Are you asking how to get the video that is currently displaying on YouTube onto your computer and into Premiere Elements 11 for you to edit and export as you want - YouTube again or otherwise?
If so, the important question is "Is that video yours or someone else's?"
If it is someone else's then see the YouTube licensing agree which I believe does not allow for that without its approval and consent.
If it is your video, did you delete or lose the original that you uploaded to YouTube in the first place? If you have that project saved, there is no reason why you cannot just edite that Timeline and upload the edited version to YouTube. At YouTube web site you can leave the original there or delete it once the edited version of it is uploaded there.
Please supply more details.
What computer operating system is your Premiere Elements running on?