I'm confused!

A proper electrical system includes:
1. A 'good' alternator core.
2. A 'good' regulator, with brushes making proper contact.
3. A 'good' battery, capable of holding a full charge.
4. 'Good' wiring connections between the battery, alternator and ground.

You should read 13-14 volts at idle with no large loads such as headlights, blower motor on high, or rear defogger. 11 volts at idle means either the alternator/regulator is not producing a charge, or the battery is not taking a charge.

Let's go back what I understand that you have done so far...

1. You replaced the regulator.
2. You replaced the battery with a 'spare' battery, not brand-new.
3. You charged the battery, but only got 9-11 volts.
Was this with a portable charger, or using the car at idle?

So, we don't know about how good the battery is...