I agree with bamf, this is meant to be a fun game and this is a well known exploit.
The double move issue is a well known issue with Pitboss. There are few good games that don't try and outlaw it as far as is possible. I've been in one where it was allowed and especially later on it is very unbalancing. Your whole game can be wrecked by a double move. Later on it gets worse, no one can permenantly garrisson everything well enough to fend off a double move from someone who knew what they were doing. And losing a city or two at the start of a war, especially if that has some vital war making commodity, is crippling. And don't think you can counter attack to recover from it. It will be razed....
There are two big exploits of the pitboss system that can happen in war time and both are usually considered illegal. And they are both due to the nature of Pitboss and so unique to it. Double moving (like in this case) and partial moving but not ending your turn. e.g. when you make moves (either offensive or defensive) before your opponent has a chance to respond to your last move but you don't end your turn. Then after his turn go back in and complete your turn. It's sort of like double moving but even stronger as you both double move your opponent and get to make some final adjustments after his move to attack or reposition again. The main advantage of Civstats is to track these abuses.
I appreciate, Zen, that you may not have been aware that what you were doing was considered an exploit by most Pitboss players. So lets just replay the turn. Misunderstandings will happen and are likely to again, but it can be easily sorted out in this case.
It doesn't leave you in a bad position. If you have an ally you should still be able to take him out without resorting to using tactics most people consider cheats. If you think his capital is too strong to take then you can at least stop him building Immortals and so neutralise him. So the war under it's original stated aim will probably succeed. Once you have a counter to Immortals you can either take him out or make peace.
And to Ulfang - yes this issue is due to the nature of Pitboss. While you could just "live with it" I think Pitboss would die off if no house rules of player conduct were followed. So most of us accept the need for a couple of house rules in return for the much faster game play that Pitboss gives over PBEM. It's not much of a restriction, you couldn't exploit PBEM or the AI like this so we are not taking away anyones favourite strategy.
And as Bamf says if you play at the same time every day it is unlikely that you ever need be inconvenienced by this as you won't be double moving anyone that way. And outside of war you can double move to your hearts content.