I'd put the multimeter on it ... sounds like it's solid on acceleration, bounces at idle? ... how old is the alternator?
While it's running at a higher idle, set the meter to DC voltage, put the red lead to the back of the alternator connection location, black to the housing. Do the same at the battery. You should see the same reading - 14+ volts.
BTW, they'll test your alternator free at the auto parts store. PLUS, they'll hop right to it if you show up in uniform AND of course with the car. Both of those are "attention getters" for most people.