Your diode breaks everything. *OK, not everything, but...
Depending on its orientation, you will either never be able to use the onboard
battery, nor correctly charge it
(or will overcharge the outboard battery if the onboard charger is set 0.6V high)
--or--
you will discharge the onboard battery and never be able to charge it.
The diode limits current to one direction. It further accounts for a 0.6V (nominal) voltage drop across the diode.
You want to parallel the batteries plus-terminal to plus-terminal and minus-terminal to minus-terminal, direct.
You also want "identical" (as near as practical) batteries, obviously technology (SLA vs NiMH vs LiIon), but also
rated capacity. Don't parallel a 3AH internal battery with a 120AH external battery and expect good charge results.
-RDH