As Kovid says, you will not be able to have a single library, as it calibre cannot have multiple users at the same time for the GUI.
I have a not dissimilar setup, except the family I share with are vampires and don't do metadata cleanup in return
The key feature to use is Save to Disk as your sharing mechanism. So as one if you completes a set of books, you export from calibre using this feature to a shared network sub folder. This will by default export the formats, cover and metadata file for each book. The other person then uses the Add books from folder, one book per sub folder option to import them into their library. I suggest they move the books out of the shared folder first, so you import just that batch only once.
With two of you doing cleanup, you will probably want to have two shared folders, that act as output for person A and input for Person B and vice versa. You will want to make sure you have exactly the same calibre schema so any custom column data gets imported. You will also want to setup Automerge to overwrite books, in case the other person sends an updated version.
Then the final issue becomes how to partition work in progress books from finished ones, so you don't end up with a bunch of duplicates. For instance if you both started with the same messy library copy, and cleaned up different authors and imported each others work you could get a bit of a mess.
The answer to that depends on your starting point. If the books are already in calibre, I would have two libraries each. One is the raw mess as a working library, the other is your lovely clean library. So the workflow is you tell the other person what author you will work on, you cleanup the data and book in your working library, use Copy to library option to put in your own clean library, then Save to Disk to put in the folder for the other person. Their workflow is to delete any books for that author from their working library (optional), switch to their clean library, and Add as described above. That way at any point you both have a clean library you can open contains your perfect books and you both have the raw books.
Alternatively you could try to do the cleanup in a single library each, with a custom column and the restrictions drop down. You just need to make sure you delete books for the author before you import from the other person to prevent a mess of duplicates due to title and author variations.
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