This can be solved using synclient:
synclient -l to list your configuration. At the end of the output, you will find something like
RightButtonAreaLeft = 3068
RightButtonAreaRight = 0
RightButtonAreaTop = 4326
RightButtonAreaBottom = 0
These values have to be changed to 0 (zero) by typing these two commands:
Clicking anywhere on your trackpad will now always trigger a left-click. To right-click, do a two-finger click on your trackpad.
To make these changes permanent, write the two commands to a shell script and add the script to your startup applications:
Paste this code to the shell script:
Open the Startup Applications program in Unity and add ~/.synaptics-custom-settings.sh to the list of startup applications.