Custom post type templating problem

Archive pages A & B already exist as your brand and type term archives, you can style those differently by creating taxonomy-brand.php and taxonomy-type.php templates.

The remaining piece is two different single product views. The simplest way to achieve that would be to append a GET var onto the permalinks:

http://domain.com/product/someproduct/?origin=brand
http://domain.com/product/someproduct/?origin=type

WordPress has the built in function add_query_arg to help add that for you:

echo add_query_arg( 'origin', 'brand', get_permalink() );

Then in your single post template you can check the value of $_GET['origin'] to determine what to display in the sidebar.