How do I embed an entire website into another through a VPN or other unblocking method?

I am trying to embed YouTube into a website so that my friends can watch it at school without everyone having to set up a VPN. This will make life easy for everyone as people can just visit a link and access YouTube- where it would normally be blocked. I know this can be achieved as a service called MyEd does this allowing teachers to add YouTube videos (full player and everything) and for students to watch them without a VPN.

If you need a summary: I am trying to create a website that has YouTube inside it, which is unblocked (so no JS iframe)

It would be great if anyone could help. Thanks.