Voltage Controlled Voltage Source Circuit Analysis
the current from the VCVS[sic] would have been 1.003 * 10mS = 0.001003.


Why do you say that? 

The voltage being sensed by the VCCS is the voltage from source V1, minus the voltage across R3. 

If you want the output of the VCCS to be \$1.003 \times 10\ {\rm mS}\$, you should connect the negative terminal of the sense input of the VCCS to ground, not to the node between the VCCS output and R3.

FWIW, I hand-calculated the result based on the circuit you presented, and I also got 4.8 mA for the VCCS output current.