Check charging system, only when air conditioner is on?

Car: Ford Taurus '07

Every time I turn on the AC, almost immediately, the battery light comes on and the dash says "Check Charging System." Turn off the AC and the light goes off. Power windows are fine, windshield wipers are fine, car starts up fine, everything's working just as it should.

Cleaned the terminals (there was some corrosion), but it's still happening.

I can drive it for miles and miles and miles without anything happening, even with the headlights on, which makes me think it's not the alternator… At least I hope not, because that's a little expensive ($150-$200 for used part and labor is a lot for us right now).

What do you think? I'm taking it in on Wednesday but would like an idea of what to expect. I don't trust mechanics

Added (1). Wanted to add, it's not that I don't trust mechanics so much as it is every past one has screwed me over. I know that's not all mechanics - I've just had bad luck it seems. So I would like to have an idea of what it's going to be so I can judge if they're yanking my chain.

Added (2). Another additional detail, this has been going on for about a month and a half, and has not seemed to get any worse. Honestly we should have fixed it a long time ago - I know.

Have your alternator and battery tested at an auto parts store.