It sounds like most of the short-term emergency things could be fixed with a more steady income stream. [ $30K ] a year in a low cost of living area goes a long way compared to being homeless. It makes the car run, gets a Chromebook, plays for a cell phone plan with tethering.
I'm a programmer. I love it. As a teen I did manufacturing for six months, and I hated it. So I certainly understand grabbing a low skill job right doesn't look attractive, but it would stop the financial bleeding, and prevent things from getting out of hand while they find a software dev job.
On the immediate food side, I don't know about Chattanooga, but my town has super tiny food banks all over. There's not one centralized organization, and almost all of them are stocked at any one time. The are mom's on Facebook groups who keep track of them, and restock when low. (Some are as simple as a fridge on the side of a building, or a little library style box on a pole.) Most aren't listed on google. Not sure how to find them outside of asking around. Chattanooga has nine food banks listed on google. Odds are that they aren't all out of stock.
Good luck to both of you.