You cannot import project from Premiere into Elements and vv.
Welcome to the forum.
As Ann says, there is not much X-platform functionality between PrE and PrPro.
Also, a PC PREL (PrE's Project file) is not X-platform compatible with Mac, even with the same version of PrE installed. I think that this would be a deal-breaker for the workflow that you outline.
Once, it was fairly easy to go from Premiere (not PrE, and before PrPro 1.0, to PrPro 2.0, both PC-only) Projects on a PC to a Mac and vice-versa. If going from Mac to PC, the Project file's extension needed to be added, but other than some Transitions and Effects, that might exist on one platform, but not the other, the files were easy to Open and edit.
For a period of time, a PREL (PrE's Project file) could be Opened in PrPro, so long as the versions of the two programs were somewhat contemporary, i.e. PrPro 2.0 could Open PrE 4.0 PREL files, so long as there were no Themes, Instant Movies, or some 3rd party Transitions/Effects, such as NewBlue FX's.
That does not seem to be the case with at least PrPro CC, but maybe those reporting on the incompatibilities did not have "plain vanilla" PREL's? Nowadays, I rather doubt that there IS much compatibility between PrE and PrPro, but am not on CC, so I cannot test that completely.
Good luck, but I do not see what has been proposed working well, if at all.