I know a lot of people like to hate on Napa, but the one here in Louisville has always treated me right. You can drive your rig in there, and they can determine if it's likely a battery problem or not on the spot. If it's not a battery issue, you can bring the alternator in there and they can test that for you. At least that might save you some time determinging where the problem is.
As for re-building, I don't know. With past vehicles I've always just bought re-man. alternators and never had a problem with them.
Also don't know much about multi-meters. I use mine about once a year, and always have to re-acquaint myself with it.