Can i connect from client PC to server PC that at the same time that server PC connect root PC?

First of all sorry for my bad english and let me explain my question,

I have three entities :

1. User - He connect to www.example.com
2. Web Server ( www.example.com ) - He can connect to www.private.com
3. Private Server ( www.private.com ) - He can be connected through allowed IPs

So i want that User connect to www.example.com and through something connect Web Server to Private Server and display one page .

I have tried through iframe , but unlucky thing

How can i make that connection ?