ECM issue or not?

I purchased a 2012 Jetta in October. I've yet to drive it, it's still in the shop. Bad research and choices on my part, but on to my issue:

At first the car wouldn't start unless it was jumped, was told it needed a new battery, so I got one. Dash lights come on, car won't start. Take it to a mechanic, and I'm told it's the alternator. Got a new alternator. Car starts, but after 10-15 minutes of driving the battery light comes on- it's not charging. I take it back to the mechanic. Car sits for about 3 weeks, I call him, and find out he hasn't done anything yet. Tells me it's the electrical system, he's checking some wire stuff, should be fine.
Fast forward to today. He hasn't called, I just show up at the shop. It's the ECM now he says. Tells me when I got the battery at Autozone they switched the terminals and burned the old alternator and blah blah blah.

Obviously, if the same person tells me it's a bunch of different things and none of them fix the issue, it's time to take it to someone else. I don't want to spend the $1200 he's quoting me on an ECM I can't be sure will fix the problem. My question is: if the car does start but won't charge, can it possibly be the ECM? Keep in mind new battery and alternator.