I know the catalog cannot be shared between these two programs, but what is a good way to have them coexist together? It seems like I would have to have a separate copy of my photos that each program would use. I use Lightroom, but looking at picking up Photoshop Elements and Premiere 10.
If you install both programs on the same computer, you can open the images in Photoshop Elements directly from within Lightroom. See instructions here or google "lightroom open in photoshop".
The advantage of this (compared to exporting the images, then opening in Phososhop) is that the *.PSD files are automatically accessible from Lightroom's catalog, and can (optionally) be stacked with the original RAW images, making your workflow a lot simpler to manage. You can also add metadata to the linked PSD files.
Photoshop Lightroom does basically everything a photographer would want as compared to what Elements can do. If there is a specific feature you want in Elements, just export from Lightroom as a JPG and make your edits in Elements, then pull it back into Lightroom. No specific workflow is needed.
Personally, for photography I rarely use Photoshop any longer, as Lightroom will do about 95% of what I need to fully ingest/asset manage/backup/edit/print a wedding shoot.