No, there is nothing wrong with HTTP request. Don't jump to conclusion if you don't know what you're talking about.
You get server error 500 from TunIn API, because you have replaced wrong bits of the url. You should have replaced whole "<id>", "<key>" and "<stationid>" with your values.
Your data.txt contains only combined title. You should try to use custom data field in RDJ and see what gets saved in data.txt. If custom data doesn't provide artist and title (it should), you'll have to parse artist from combined title.
To make script a bit more foolproof, here it is with API keys moved to the top:
<?php
// TuneIn API settings
$StationID = "s######"; // TuneIn station ID
$PartnerID = "########"; // TuneIn partner ID
$PartnerKey = "_########"; // TuneIn partner key
$artist = isset($_REQUEST["artist"]) ? urlencode(stripcslashes($_REQUEST["artist"])) : '';
$title = isset($_REQUEST["title"]) ? urlencode(stripcslashes($_REQUEST["title"])) : '';
// Save data for troubleshooting
file_put_contents( 'data.txt', print_r($_REQUEST, true) );
if(empty($artist) ||empty($title))
exit('No data to send');
$url = "http://air.radiotime.com/Playing.ashx?partnerId={$PartnerID}&partnerKey={$PartnerKey}&id={$StationID}&title={$title}&artist={$artist}";
echo file_get_contents($url);
?>