OK, I'm really stumped as to why it's not there... But here are a few things that might help. First, to get rid of the Sign-in request.
Go to your Gallery App, hit the Menu button, and select CONTENT TO DISPLAY. There, disable the Picasa option (once we get rid of her accounts, you can re-enable that if you want to see your Google+/Picasa pictures in your Gallery).
Now, odd question. If you go into YOUR account, do you see a REMOVE ACCOUNT option?
Even odder test, on her account, have you tried rotating the phone (hold it in landscape)? Or change the font back to the stock one instead of the Chococookie one?
If none of the above work, try long-pressing on the account while in the Account screen or hitting the menu button in that screen to see if you get an extra menu. From screen you disabled all the sync options, are you sure there's no three dots or menu with the menu button with that option? That's where it should be!
Lastly, I'd try going to Settings, General, Security, Device Administrators. Is there anything there that might be associated with her account? If so, that might be preventing you from removing it (which would mean, I think, that you would be able to remove yours, but not hers).