What computer operating system is your Premiere Elements 9 running on? And, are you running Premiere Elements 9 as the 9.0.1 Update version?
What are the properties of what went into the Timeline of this 30 minute project?
a. one jpeg photo, what are the pixel dimensions
b. 20 second video clip, what video compression, file extension, frame size, frame rate, interlaced or progressive, pixel aspect ratio.
c. and, what makes up the rest of the 30 minutes with regard to format and properties?
If you did freeze frames, did you deinterlace them or did they not appear to need editing? Is "video is mpeg" what takes up most of those 30 minutes? If so, properties, please.
When you describe the final product as shaky, is the shaky at points in the video where the most motion exists?
Now backing up to the beginning...what did you set as the project preset for this project based on the properties of source which appears to be the "video mpeg"?
Do you always run into the above issue with your burn to DVD-VIDEO on DVD disc? Or, was it just this one project?
Please review and consider and then we can decide what next.