2013 Dodge Grand Caravan Battery Light

Wife called me, said battery light was on. I told her
it was either alternator or battery itself. Since she
just started the van and drove off in it, I guessed
alternator.   We had just had that replaced a little
less than a year ago at a Firestone shop. I called
them and asked about warranty. It was covered,
along with the tow bill to get the van to their shop.
They replaced the alternator and charged the
battery. All checked good at that moment.  I show
up later that evening after work to pick up van and
the battery light comes on and stays on. I had
Firestone recheck everything again and they said
alternator is good, but battery was only clocking
around 500cca's, it is actually rated at 750 CCA.
Mechanic said it was fine to drive and that the
alternator going bad could have damaged the
battery. He said to drive it for a few days to see if it
would charge on up and shut off light. If not, I may
need a new battery.
We drove van for over 2 weeks, like normal, with
battery light on and some cold temperatures days
too. No problems, other than light staying on.
So I took battery to Walmart, where they tested and
said it was bad and prorated the price of a new
one.
I installed it, cleaning the post and connectors.
Everything looks good there. The battery light still
stays on.
What now?  Possible bad new battery from
Walmart? I don't think the alternator is problem,  
because we continue driving it, operating electric
doors, rear hatch, etc, with no problem other than
battery light is on. Van starts every time we try it,
even in cold weather. 20 degrees this morning, and
it had not ran all weekend. Started just fine.