Is it possible to hide the page within the sub-site but only allow a unique group of people to access that page and the documents within it. This is also within a sub-site.
You can set unique permissions on web applications, site collections, sites, libraries/lists or single publishing pages, documents and list items in SharePoint.
Site permissions is controlled under Site Actions > Site Permissions
Permissions on lists is set on libray/list settings > Permission Management > Manage permissions for this library > Stop inheriting permissions. After this you can add/remove permissions to suit your needs.
Permissions on pages, documents and list items is set either in context menu for a specific item/page/document or by selecting an item and clicking Document Permissions > Stop Inheriting Permissions. After this you can add/remove permissions to suit your needs.
Since SharePoint trims the GUI so that you dont see links to pages you cannot access, the page will become hidden for users that do not have access.