You realize, don't you, that you are legally responsible for the car, and if (heaven forbid) the kid is driving and the shoddy repair gives way and he gets hurt and/or hurts other people, you are on the hook?
I also have an ex and a teenager who lives with me, and a lot of stupidity about money and so on.
You're better off getting your name off the title and the kid off your insurance. Get the car back, take it to a decent shop, fix it if you can afford it, if you can't afford it, get it off the street. Don't argue money with the kid's other family - bad all around. Don't give the car back to the kid, sorry. "It's not safe" is a really good excuse to keep it away from him.
There is no way you can "win" in a situation like this. No matter what you do, you're the bad guy. The best you can do is cover yourself. He hasn't shown the maturity required for you to trust him to drive a car in your name. And get him off your insurance NOW. That just leaves you open to all sorts of issues. If this is the way he acts in an accident, you don't want him anywhere near your insurance policy.
Good luck.