It is entirely possible to play Civ V using the Remote Desktop Connection that comes pre-installed with Windows starting with XP.
To do this, you need to first configure the server (in this case, your computer) to allow remote connections to it. After that, you'll want to use the Remote Desktop Connection app on the Notebook to connect to the server.
In order to play at the same time, you'll need to create a second account for your wife on your computer (if you haven't done so already). The reason for that, is that Windows does not allow access to one account using multiple terminals (including local access) at the same time; i.e. if you try to connect remotely to your own account while you're still logged on locally, you will be locked out locally and vice versa.
The performance when playing Civ V remotely is not much of an issue, since the game is entirely turn based. Depending on the connection speed and quality, you will notice compression artifacts, especially around text, which will disappear over time so long as the image doesn't change too much; because of this, playing Action games remotely is not recommended unless you have a very fast and reliable local network (802.11g is a bit slow for Full HD, but acceptable for Civ V).
It is possible to experience lags (most noticeable by listening to the in-game sounds) during the remote session, but this shouldn't be too unbearable.
Unfortunately, since I do not own multiple copies of Civ V, I couldn't verify if it is possible to run two separate instances of the game on the same machine.
Depending on how Microsoft implemented the Remote Desktop Connection, attempting to run multiple instances of a game remotely may result in one of those three outcomes (there may be more or less than three):
- Both instances may run at a reduced performance similar to playing at double the resolution (ideal case)
- One instance may run at almost full speed (GPU accelerated) while the other will be extremely slow (rendered by CPU)
- One instance will run at full speed; the second instance will be unable to claim DirectX ressources for itself and will therefore be unable to launch (worst-case scenario; maybe playing in borderless windowed mode can fix this?)
It is unlikely that using two or more GPUs will change the outcome.
Keep in mind, that just because Civ V can be launched over Remote Desktop Connection, it does not imply that other games will too. For instance, two games I've tested, Just Cause 2 and Roller Coaster Tycoon 2 will refuse to launch over a remote connection. Funny fact: it is possible to play Roller Coaster Tycoon 2 remotely, as long as it runs on a Virtual Machine and you are not directly connected to it via Remote Desktop Connection.