Can I be honest with you? This is never going to end happily for you, and you need to start being a bit more assertive matey.
Even if he does fix the car, do you think it'll be actually fixed or just 'fixed'? It's going to be the latter, and then if you've paid half the cost you're taking some of the burden when then trying to get it properly fixed. Sometimes you just have to cut your losses and run, and this is one of those times.
Reject the car, and give it back to them. Send the letter. Start court proceedings. You have a solid case here, there is no way the result will go against you, so stand your ground. Yes it can take a while, but better that than being stuck with an utter lemon.