Arduino 2 power source - auto switch?
I have done something similar because of a charging module I placed in my design and the answer was to go with Power Path instead this was done with the LTC4412 powerpath controller and worked fine.

The big reason I had to go there was to be able to switch the connection between my batteries between series and parallel as I had to charge them in parallel and use them in series.

The LTC4412 is very small and with very few external components it is easy to accomplish the power path.

Here is a datasheet for the LTC4412. 

Take a look at the FET specs. I had to go with a bigger one than the one they used in their application notes.