Connect another DB and fetch records from some tables

here is what I did with slight change as per your need. May be it will helpful for you. 🙂

function fetch_news()
{
    global $wpdb;
    $wpdb_backup = $wpdb;   // backup existing instance
    $wpdb = new wpdb( NEWS_DB_USER, NEWS_DB_PASSWORD, NEWS_DB_NAME, NEWS_DB_HOST ); // create new db instance
    wp_set_wpdb_vars();     // add variable

    $news_sql = $wpdb->get_results("SELECT * FROM rss_news");       // your query to external db table using $wpdb object
    or
    $news_sql = mysql_query("SELECT * FROM rss_news");      // your query to external db table

    $wpdb = $wpdb_backup;   // restore old instance
    return $news_sql;
}