Stan nailed it, encode direct to MPEG-2 DVD from Premiere, using Media Encoder. However, in regards to the current render looking bad, your source is 16:9 but it looks like it is being encoded as 4:3 and that could have some negative effect. So choose the "MPEG-2 DVD" format, and then the appropriate preset, such as "NTSC Widescreen Progressive" to create the assets to import into Encore an make sure to keep it all 16:9 throughout the workflow
Thanks
Jeff Pulera
Safe Harbor Computers