It's because you aren't escaping your quotes. - \" instead of " (when you want to have the quote there). So:
HTML Code:
$rss2_output .= "<dt><strong><p style=\"color: sienna; margin-left: 20px\">
<a href='" . trim($link) . "'>" . htmlspecialchars(trim($title)) . "</a></p></strong> - " . htmlspecialchars(trim($date)) . " by <em>" . htmlspecialchars(trim($author)) . "</em></dt><dd>" . htmlspecialchars(trim($description)) . "</dd>";
You probably need to put the color inside the <a> tag. Also, don't use <p>, use <span>.
HTML Code:
$rss2_output .= "<dt><strong>
<a href='" . trim($link) . "'><span style=\"color: sienna; margin-left: 20px\">" . htmlspecialchars(trim($title)) . "</span></a></strong> - " . htmlspecialchars(trim($date)) . " by <em>" . htmlspecialchars(trim($author)) . "</em></dt><dd>" . htmlspecialchars(trim($description)) . "</dd>";