passing URI /path to server when loadbalancing

HTTP::redirect is a shortcut for sending a 302 (Temporary Redirect) back to the client without involving the server that has the application. This is the reason why a different name is in the browser.

when HTTP_REQUEST {
 if { [HTTP::path] equals "/uat/login"} {
   node servername 10444
  }
 }

This will send the request on to the server.

I don't really recommend node. I'd use a pool and the pool command

pool servername_pool