You are saying that separating power supplies might be the way to get the total current usage low enough to make the servo work? I would prefer to use the same power supplies and I am wondering why it is working with the nano, but not the pro mini. I thought the only difference was the USB jack. Sorry to repeat that, but that is my main question I guess.
I did forget to mention the removed regulator. 
Another thing I forgot was in the drawing - to add the decoupling capacitor to the servo. This was required to make the servo non-jittery (with the nano). In fact a 1000uF capacitor was not enough. The next size up I had was a 2400uF, which smoothed out the servo and PIR operation nicely.
According to the site (http://www.home-automation-community.com/arduino-low-power-how-to-run-atmega328p-for-a-year-on-coin-cell-battery/), removing the regulator will save only 18 uA in sleep mode, so yes maybe I shouldn't remove it when my next minis arrive. However, the range of processor operating voltages is 1.8-5.5V with an absolute maximum of 6V, which means I should be able to power if off either the battery pack or the DC power pack because both are 5.3V after the diode.
Chris please note that I didn't have 2 battery packs in the diagrams, it is 1 battery pack and a DC pack.
I plan to rebuild the circuit as per either diagram A or B in post number 5 at:
http://forum.arduino.cc/index.php?topic=422160.0
However, I plan to incorporate a 3 pin DC jack in either a battery charging or battery elimination setup. Thing is, only the battery elimination part I understand so far. I would like to understand how to charge a LiFePO4 battery this way. Float charging a single or double cell up to 90%. I learned a couple of things from the following forum post about float charging a LiFePO4 battery as being similar to charging a capacitor and being able to leave the charger connected to the circuit.
http://forum.arduino.cc/index.php?topic=425890.0
http://electronics.stackexchange.com/questions/90529/what-to-do-with-third-contact-in-dc-barrel-plug-with-only-two-input-contacts
https://www.sparkfun.com/products/10785 (discussed in comments section)