"I have many old VHS tapes that I copied to DVD"
It looks like he has already moved the video from VHS to dvd disks. His problem is that Premiere Elements is degrading the quality of the video, probably because it is reencoding them after he edits.
What exactly are you doing when you are editing? Are you just cutting out sections or are you doing something more intensive?
You might try the free trial of Womble Video Wizard DVD, just to see if you get better results. Here is the link
Edit: I've got to learn to type faster