Using a motor signal to power a op amp to power another motor
You'll need some kind of control system, one problem that I see is the bigger motor also generating voltage in the smaller motor and creating a positive feedback loop. Because of this control theory will be needed to find a closed loop system response that is stable.

In my mind it would be better to use an encoder and use the position output from the encoder to control the larger motor. 

If you do need an opamp to control the motor (also look into PWM control), the output can be boosted with a bipolar output stage