How can I produce an analog control signal from -2 to 12V?
Since your immediate question seems to be how to create a "signal" that is adjustable between -2 &amp; 12 volts. I will prescribe a simple experiment which you can perform in the comfort of your own living room, and which will illustrate the basic principle. The principle is extendable to many implementations, including DACs and the like.

Hook up the pot and 12 volt supply just as you describe to get a "signal" ( actually a DC voltage) which can be varied from 0 to 12 volts by turning the pot thru its mechanical range. 

Next hook up another power supply as follows. Ideally, this would be a 2 volt supply, but it can be 5 volts or similar. An adjustable bench supply adjusted to 2 volts will work fine. Both of the power supplies must be isolated from earth ground (most bench supplies are, or allow you to do so via the output terminals). 

Connect the positive output terminal (usually red)  of the 2 volt supply to the negative terminal (usually black) of the 12 volt supply. This connection becomes your "ground" or "DC Common". Next, re-connect one end of the potentiometer between the positive terminal of the 12 volts supply and the other end to the negative terminal (black) of the 2 volts supply. 

Connect your DVM negative lead to the "DC Common" (either the red terminal of the 2 volt supply or the black terminal of the 12 volts supply) and the DVM's positive input to the pot's wiper. 

Energize the power supplies. Rotate pot shaft and note how voltage varies smoothly and continuously from minus 2 volts to +12 volts. See?

The principle is that you can stack voltage sources, one on top of the other, connected positive to negative, and add up their voltages. As long as the voltage sources are isolated, you can choose any inter-source connection as your ground or DC common. Voltage is relative - always a good principle  to remember.