Here’s a little tip for those parents who have enabled restrictions on their kids’ devices, but still find that YouTube is accessible.  I’m assuming you’ve already set up restrictions (under Settings > General > Restrictions).

The next step is to tap on ‘Add a Website’ under ‘Never Allow’. The trick here is to enter both the normal YouTube URL (http://www.youtube.com) and the mobile site URL (http://m.youtube.com), as most times your iPad or iPhone will access the mobile site.
Here’s a pic of the setting correctly entered:

The same of course applied to other sites that have a mobile version. To determine the URL for a mobile version, just tap once in the URL bar of Safari once the site has loaded, and you’ll be able to see the full URL.

Hope that helps you a little.