Alternator or parasitic drain? – Honda Odyssey 2008

uring the last hour of a nine hour trip, battery charging system light came on our 2009 Honda odyssey. We eked out the last 35 miles and got to a place that tested the 3 year old battery. It showed it all but dead and they put in a new one. Alternator in the car is less than one years old. Car started up fine and we drove it to our destination 5 miles away.
Next morning, the battery was completely dead. Had it towed to a local shop and they said it was just a loose connection. They charged it overnight and it started up again. We asked them to keep it for 24 hours to make sure, and when we picked it up this morning, again it started up without a problem.
Just drove it 2 miles down the road, let it sit for two hours and the battery is almost dead again.
If it’s a parasitic drain, why would a battery light come on while we were driving and the alternator was charging it? If it’s a faulty alternator, why would it be dead just sitting overnight. 10 hours from home and 2 days left

Brand: Honda
Model: Odyssey
Year: 2008