This could get ugly. In all seriousness, you might want to just consider swapping cables on the monitors.
What type of video card are you using (Nvidia, etc.?)
Likely what you'll end up having to do is create an xorg.conf file in /etc/X11/ (or creating the appropriate fragments of one in /etc/X11/xorg.conf.d). What you need to put in those fragments differs depending on which video drivers your using (and, thus, on which type of video card you have). Most of the time the X.org software doesn't need a configuration file these days, but in situations like this you can, and will have to, use one.
You might also end up having to change the configuration of the display manager (which I think is lightdm by default).
