Redirect based on Host Header and Hide URI?

HTTP::redirect actually sends a redirect to the client's browser, so with that method you won't be able to get around the user seeing it. You could try simply modifying the URL (specifically, the uri) before forwarding it to the pool, though. It would appear to the user that the path is just "/", which of course is the root directory (default when no path is specified).

when HTTP_REQUEST {
  if { ([HTTP::host] == "app1.example.com") and ([HTTP::uri] == "/") } {
    HTTP::uri "/dir1/dir2/index?id=1?=0"
  }
  if { ([HTTP::host] == "app2.example.com") and ([HTTP::uri] == "/") } {
    HTTP::uri "/dir1/index?id=1"
  }
}

When the user clicks additional links or sends a post or something, the URL will be adjusted in the user's browser accordingly, but this would at least hide the first path from the user on initial connection.