As you have now stated that both Theme A and Theme B are already Child Themes, perhaps you could try adding this to your funcions.php file in Theme B –

add_action('wp_enqueue_scripts', 'enqueue_front_scripts');
function enqueue_front_scripts(){

    /** Switch to the parent blog */
    switch_to_blog(1);  // You may need to change the ID, I don't know what ID you main site has
    
    /** Grab the path of the parents 'header.php' file */
    $main_header_style_path =  get_stylesheet_directory_uri() . '/header.css';

    /** Restore the current blog */
    restore_current_blog();
    
    /** Enqueue the main header styling */
    wp_enqueue_style('main-header', $main_header_style_path);
    
}

function get_main_header(){

    /** Switch to the parent blog */
    switch_to_blog(1);  // You may need to change the ID, I don't know what ID you main site has

    /** Grab the path of the parents 'header.php' file */
    $main_header_path =  get_stylesheet_directory_uri() . '/header.php';

    /** Output the main header */
    require_once($main_header_path);

    /** Restore the current blog */
    restore_current_blog(); // Don't restore until after you have included the header, otherwise you 'get_blogino()', etc. calls will reference Theme B
    
}

And then to include both headers you’d do this (note that the header file in both themes would simply be called header.php) –

get_main_header();
get_header();

I suggest that you have a read of the Function Reference for switch_to_blog() for more information.

Update

I forgot to mention that you would also still need to seperate your header styling in to it’s own header.css file in Theme A, and then enqueue this in both Theme A and Theme B.

I have update my code example about to reflect this.