Out of luck, unless you are PHP-savvy enough to mess around with the scripts a bit. Or unless you choose a different CMS software.
I've had the same problem (fortunately those were on sites I made, so I could just rewrite it). allow_url_fopen is what determines whether you can use file() to read an external web page. For example, file("http://www.google.com") would return the content of that page, if allow_url_fopen is enabled.
It's disabled on DH, and you need to use the cURL library instead. If a software you're trying to use can't cope without allow_url_fopen and doesn't support curl, then you won't be able to use it. (If you know PHP, you could dive into the script files, see where the function is being used, and rewrite it using the curl functions.).
Personally, I recommend the Drupal engine, which has no trouble with this. But if you were using EzPublish before now and are just moving the site to this server, then migrating to a different CMS is difficult.