Hi,
My wife and I both play CN and have separate nations. I log in from my work computer and she uses our home computer to play, but we also have a laptop that I use to check my nation whenever I am out of town.
Today, my wife wanted to use the laptop to log into her nation from our home wireless network and entered her nation name and password but somehow she got logged into my nation. She does not even know my password so I am not sure how this could have happened. She immediately logged out but she is now worried that we will have both of our nations deleted because of what happened.
We have both played for over two years and this has never happened before.
Are our nations toast?

Well, if this doesn't happen again your nations will be fine. But it's possible that the game will not let you trade/aid /war together etc. each other anymore.

Correct, if your nation was logged in at home then you will not be able to trade/aid/war together ever again.

However, as long as this doesn't happen again (e.g. you only log in from separate locations in the future), you should be fine as far as deletion goes.

The browser you're using on your laptop is probably set to save your passwords. For an incredibly long list of security reasons (of which CN is probably one of the less important) I recommend to disable that "feature" and to erase all your saved passwords.

If you want to retain the ability to save your passwords, at the same time having little to worry for your accounts' security, I suggest that (1) you use a browser that supports profiles and that (2) you protect your passwords with a (strong!) master password.
This can be done with Firefox and probably with other browsers (you can do a search about it, or you can send me a PM - the second being a slower and less reliable method).