Getting one specific value from get_children array

If you want to query by a post author , you can try the author input argument:

$sub_orders = get_children( 
    array(    
        'author'      => $seller_id,
        'post_parent' => $reservation->transaction_id,    
        'post_type'   => 'shop_order',    
        'post_status' => array( 
            'wc-pending', 
            'wc-completed', 
            'wc-processing', 
            'wc-on-hold' 
        )
    ) 
);

Note that get_children() calls get_posts(), that is again a wrapper for WP_Query, so you can use the author_name, author__in and author__not_in input arguments as well.