How do I make it impossible to move an Internal Frame?

There are multiple ways to do it. You could simply override the setBounds(....) method and always ignore the changes in x and y coordinate. Other alternative is to install a DesktopManager subclass in the JDesktopPane to which the JInternalFrames are added and override the
public void setBoundsForFrame(JComponent f, int newX, int newY, int newWidth, int newHeight)
to ignore the newx and newy.