Arduino Circuit Power Redesign

I'm a beginner attempting to make this pictured circuit. The author of the schematic powers Arduino through the circuit but I am curious if I can do the opposite and power the circuit from the Arduino. If I were to attach a 12V power supply to the barrel jack of the Arduino and reverse the diodes from the VIN Pin. Any help or points in the right direction would be greatly appreciated. Thank you.

Link to larger image.

The Arduino only outputs 5V and 3.3V. The 12V must be externally sourced.

MarkT:
The Arduino only outputs 5V and 3.3V. The 12V must be externally sourced.

I would use an 12V external power supply and connect it to the DC barrel power jack. I was under the impression that I could then access that power from the VIN pin. Is that not correct?

You would end up with the barrel jack voltage less the voltage drop across the reverse polarity protection diode (up to 0.7V, will vary with overall current being drawn) up to a max of 1A.

It may vary depending on the manufacturer of the board. Vin is connected to the center pin of the jack on most but on some it is connected downstream of the diode. You need to check this with your ohmmeter.
Good Luck & Have Fun!
Gil