RossMitchell on "send mail or create restricted access user role? experts advice needed"

Each approach will have its own different challenges.
I would go for (2) as being more flexible, more general. You will have a supplementary user table which maps wordpress user ID to product category groups.
In your plugin register a shortcode for your restock product report, it checks that the user is logged in, and does the report for their products.
Producing a weekly email is technically reasonable, but is immersed in managerial issues, just when does it fire ? Inevitably people will want refreshes, and so on.