Last August we purchased a matching pair of Rad Runner + ebikes for my wife and I. I ride my Rad Runner + much more often (and much further) than my wife and therefore charge my battery more often. Would occasionally swapping her less used battery with my higher mileage battery effect the digital memory on the bikes with regard to each bike's accumulated mileage?
No, bike mileage is not stored in the battery. Have seen mention of memory resetting mileage to zero if the display is not turned off before turning off the battery but using her battery should be no different than taking yours' off to charge and putting it back on.
Yep, mileage is stored in the controller system; that reset-to-zero thing is a rare glitch that I see people mention every now and then, but it's not common.
FYI, if you have a bike that can use the 35A controller upgrade, your mileage will restart at zero of course, so I made a note of my end reading when I did the upgrade. The good news is that the trip odometer on the new controller doesn't reset to zero after power off or even the timeout period - that used to piss me off mightily about the stock display when stopping for a pee, errand, lunch or coffee break.