Something in the description of your workflow doesn't quite go with my understanding of how Lightroom works. If Lightroom gives you the option to include the Lightroom adjustments, that means that Lightroom is going to create a copy of your original image that includes the Lightroom adjustments you have made, and then sends that copy to Photoshop Elements. The idea is that your original (master) images are never actually modified. Lightroom just keeps a history of the adjustments that you have made using Lightroom. So when you save your work in Photoshop Elements you should have a second copy of your image; the original and the one that you modified in Photoshop Elements. If that copy is not being displayed next to the original then perhaps you should change your sort order to filename. Then they should appear together in Lightroom in a stack that can be collapsed so that you only have to look at the one image.
The image that Lightroom creates and sends to Elements should either be a TIF or PSD file, and that depends on the options that you have set in Lightroom (Preferences/External Editor).