No, the "two stators" thing (on the Honda singles and twins of the 60s & early 70s) comes from the fact that they had two separate windings within the stator assembly. Both windings fed to the rectifier and then to the battery & loads. However, when the headlight was switched off (back when you COULD turn the headlight off) only one of the coils fed the battery. When the lights were switched on, the 2nd coil was joined with the first to BOTH feed the battery & loads.
For troubleshooting, my favorite technique is to clip a cheapie voltmeter to the battery, tape the meter to the tank and go for a ride! Watch the battery voltage as you ride in the real world. It should be showing 13+ volts at above-idle speeds as a minimum.
If it does read above 13 volts and you're still not holding a charge, then your battery just isn't holding a charge. If it doesn't read above 13 volts, it's either a bad battery that just won't TAKE a charge, or, most likely, something in the rest of the charging circuit.
For the rest of the circuit, there are 3 major parts: the stator/rotor combo, the rectifier and the voltage regulator.
First, I'd do an "open circuit" test of the stator/rotor combo. Unplug the connector and, using a meter set to AC volts, run the motor and measure between the pink and yellow wires and the pink and white wires. You must read some 'good' AC voltage. Anywhere from 20 ~ 80 volts AC, depending on engine revs.
If there's no AC output, you've found the problem. If there IS AC output, then either the rectifier has a bad diode(s) or the regulator has failed.
And of course, a good strong battery at the beginning is an absolute must and cruddy connections should be the very FIRST thing to check.
Good luck with it!
Kirk