What you want is to perform DNS manipulation. In order to do that (for both http and https) you'll need to run their DNS traffic through a device that you control.
There are lots of ways to do such a thing. Your router may support web site redirects in the administration page. Another way will be to set up a DNS server on your network and configure it to bypass everything except youtube.com. You'll also need to configure your DHCP server to use your new DNS server as the default.
There's a device that will handle this for you, although it may be tricky for you to set up if you're green.
http://hakshop.myshopify.com/collections/wifi-pineapple-kits