There is one part that has not been mentioned (at least when I read the answers) and that is the voltage regulator.
On Fords, I replace it too when I do the alternator.
Now the thing is that if the regulator is bad, it can ruin a good battery as well as the alternator. I don't find them expensive to replace.
Because the engine lights would dim with low RPM's, I think there is a problem with the charging circuit. While it could just be that the idle speed was too low, it would seem that the regulator should have compensated for it. But to tell you the truth, if the alternator was going out, a working regulator would not have keep it from failing to do its task.
Good luck, I work on my own cars. So I just take the cost of the mechanics labor and put it into new parts. Like a new alternator, voltage regulator and have the battery checked out.