How to implement access to the site on behalf of another server?

Question

firewall

Good afternoon. Please tell me how to implement the following scheme:

• There are several web servers (ex. 10.0.0.10:80, 10.0.0.11:3000, 10.0.0.15:1234) behind the VPN outside the controlled area. I can't change their settings.
  
• There is one intermediate node that has access to all these servers (VPN client), it is completely controlled. Windows OS required
  
• There is also a client subnet that needs to be connected to those same web servers on behalf of the smart host. They are on a controlled network, say 192.168.100.0/24.
  

At first, there was a decision to make an intermediate node Windows Server 2008R2, establish RDP access to it for the entire subnet and get to all the necessary web servers through the browser, but this solution seemed a little clumsy to me due to periodic freezes of RDP sessions

Perhaps it is possible to somehow do simple proxying of requests in order to open on clients, for example, immediately the address of the web server, it was routed to my intermediate node, and there the request was already sent to the target web servers on behalf of the intermediate (proxy type) and returned back to the client. Are there any options?