Another idea using an R-2R DAC.
It'll give +/- 12.7V in 100mV increments with an 8-bit digital input.
A to G are at first converted to 0 to
1.27V -1.27V by U2, a generic op-amp.
U1 again is the power amplifier, but this time its gain is set to non-inverting/inverting 10, depending on whether Q1 is switched on or not.
A to G are inputs which must be exactly 5V. If the power supply to the MCU isn't that stable, use a buffer such as the 74HCT241, powered from a precision 5V reference.
The sign is positive, when the positive input is high and is negative, when low.

EDIT:
Q1 changed to a P-FET, because it's switching a negative voltage, when the gate voltage is 5V. It needs to have a low enough on resistance and cut-off voltage. The J176, or perhaps in a pinch the J175, will do.