Yes, they are bad(You want them back or I can just recycle?), and as my first sentence says, it could be a bad regulator.
I am also saying it probably ate another battery. If you can't get the battery above 12.5 volts under load, it is toast as well.
Pep Boys and many other auto parts places will test the alternator and regulator if it is integrated into the alternator for free.
If a new alternator didn't fix it last time, I am not sure another one will.
A quick google search found a "SVX Voltage regulator" part for <$200. Not sure if that means it is not integrated into the alternator or if it is a regulator for a subset of the electrical system, but the regulator could well be the issue and not the alternator.