If I understand the question correctly, the point to answer is why range and power are increased when a second battery is plugged?
When you write that you usually ride with one battery, do you mean that it is always the same one or you alternate between the two? With Dual batteries, Bosch uses only one battery at the time, and alternates the batteries so that they are discharged at about the same rate.
If you don't alternate batteries, what you observe can simply be the consequence of using batteries in different conditions. If the battery is "used", the amount of power it can deliver is lower than when it was new. It's possible that in this scenario, the system will first use the less used battery and starts to alternate between the two once the two batteries have reached a similar tension (I'm not a Bosch engineer, that is only a supposition).
Now temperature can for instance play a role if you store the bike in an unheated area, and the second battery at room temperature: the warmer battery can deliver more power than the cold one, so the system will use the "warmest one" first.