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.

You could probably hack up my ProxyPass iRule (posted here) to do just the initial redirect pretty easily, but then you get into issues of relative URLs, etc. Let's assume a client hits http://app2.example.com/ and we don't send a redirect but internally map them to app2.example.com/dir1/index?id=1. Now imagine if there was "logo.jpg" on the app2.example.com/dir1/index?id=1 page. The client would request http://app2.example.com/logo.jpg, but how should that be translated, if any, on the way through? Should it be http://app2.example.com/dir1/logo.jpg?id=1 maybe? Or just http://app2.example.com/dir1/logo.jpg?