I do a quick grade. Then I export individual ProRes clips into a new folder on my external drive called "ProRes Folder". I am producing these ProRes clips not because my computer has a hard time playing raw, it just has a hard time doing it from my external drive.
This is where I see things going wrong. You shouldn't re-import the prores files into a separate bin.
I think the better way would be to just change the source folder of the RAW bin to that of the newly exported Prores files.
You will have to disable the initial grade you made to the timeline (Shift+D) otherwise you'll have the affect applied on top of the already graded prores files.
You should then be able to simply change the source folder to link back to the original raw files and simply apply the grades again(shift+d again) and have your original starting grade and raw files linked to the edit.
Again, making use of Resolves built in proxies might be a much better solution but i havent personally used them much so I don't have any firsthand experience with them.
With that said, however, it's odd that re-linking the raw footage to your prores files didnt work. As long as they have the same file name Resolve should link them regardless of format. I'd check to make sure that when you export you're not changing the file names (the actual names, not the extensions).