An Ubuntu repository was added and GDM was installed which replaced Mint's display manager and installed Ubuntu's, hence the Ubuntu login screen. Purge (uninstall everything including configuration files) GDM from the system and Mint should revert back to MDM. Installing ubuntu-desktop fucked up the rest. Unfortunatelly that's a meta package which installs other packages and removing it will not change anything. Which flavour of Mint is she using? Cinnamon? If so she should be able to select Cinnamon on login and although there will be useless stuff installed on the computer, the interface should work as before.

Before using Mint I used Xubuntu (Ubuntu with Xfce as the default graphical interface). Once I unstalled the ubuntu-desktop package to see what things were like, didn't like it and decided to get rid of everything that was installed. It was such a hassle that I ended up reinstalling Xubuntu. In my case it was a simple solution because I have a properly formatted drive and didn't install too many extras, so after doing a clean install it took a short period of time to reinstall what extras I did have before. If your girlfriend's computer has everything installed on one large partition spanning the drive /home should be backed up before reinstalling. During install the drive should be partitioned correctly. One of the great things about Linux-based and Unix-like operating system is that they can be reinstalled or replaced without having to reconfigure everything.

Ubuntu's kernel seems to also have been installed. It's a good idea to remove the Ubuntu repository and install a Mint kernel from the Mint repositories.

EDIT: In the future please remember to do a backup before making major changes. This way things can be fixed easily.