new module not 'COMPLETELY' accessible by non-admins

I've copied the Cases module and made some changes. New module = MyModule.

As admin everything works fine. Releationships work fine.

As a regular user, I can get to the MyModule tab, but can not see any MYModules created (by admin) in list.
Nor can the user create one. => 'You do not have access to this area.' using the left shortcut form.
User doesn't see any shortcut links (New MyModule, etc).

And user doesn't see the MyModule subpanel under contact detailview. Admin does and can use it. It works fine as admin.

Thanks,
Rey