I need to uninstall the Windows 2003 instance from my laptop which has both Ubuntu and Windows server instances installed on it. I am unsure if this is possible and what would be the best method to follow to not mess up my Ubuntu instance.
Ubuntu and Windows are almost certainly installed on different partitions. From Ubuntu, you can format the partition which Windows is installed on, then update your GRUB menu to remove it.
I would recommend using gparted for partitioning on Linux. If it isn't already installed, you should be able to locate it in the package manager. You can either format the partition and leave it alone, or you could expand your ubuntu partition to take up that new free space. Keep in mind that expanding a partition can be a very long, slow process sometimes.
To update the GRUB menu, run
gksu gedit /boot/grub/menu.lst and remove the entry for Windows Server from the list. This should be fairly straightforward, but if you get confused on what to remove from the file, comment here and we can help you figure it out.