OK - just a couple of ideas, although admittedly this isn't my area of expertise.
If you're looking for a way to check if a player is cheating (by changing their clock time) you could you ask for a check and have C2 reply with a unix timestamp from the other player's computer. If the reply time stamp was dated before the request check ping was sent, or if the time difference is too great between the computers, then there's something fishy going on... If you're concerned about general clock and time differences due to normal system errors in hardware then could you synchronize the games' timers when they start to play - like having a game time stamp that runs independently of the system the game is being played on.
Sorry - I don't know how to help with using an external server to gain the data.