voltage difference between two batteries connected in parllel
A simple diode-or circuit will handle this. Connect a diode from each battery's positive terminal to VCC; when you plug two in, only one will supply load if it's at a higher voltage. If the voltages are close or identical, they will load-share. When you unplug a battery, the other one will take over.

Charging lithium ion batteries is a complex task, best handled by a dedicated charge controller. Instead, why not use two identical size batteries, and simply swap them over by plugging one in before unplugging the other?