While you could feasibly forward the challenge / response messages through an intermediary, what you're describing is not possible. What you described is not really double-hop authentication, what you describe is trying to authenticate a single session twice. NTLM authenticates a session, and a client should not reauthenticate an already authenticated session.
That is to say that in your example after the client has authenticated with the "front end server", that front end server could not then send a new challenge.