Powering Arduino Uno and Ardumoto Motor Driver Shield
Do not supply power to both the Arduino barrel jack input and VIN on the shield!


There goes the simple answer. Choose one.

If you power the system through arduino barrel jack input, you will have polarity protection, but the voltage output on VIN pin (which also used by Ardumoto shield) is slightly lower, about 0.6V lower than the input voltage because of the voltage drop on the protection diode. 

If you have want to differentiate the supply for Ardumoto and Arduino (as described on your plan), you have to tamper the Ardumoto shield to isolate both supply. Although I never try it myself, it seems possible if you understands how L298 works.