I thought I remembered you were ambivalent about the car from the beginning. I looked for the old post and couldn't find it. Sorry if I remembered wrong. But it sounds like the transaction was between your son and his grandfather. So, if this is the case, you were on shaky ground from the beginning.
Did grandfather talk to you and your husband before this offer was made, to ask for your input? Because it sounds like an accident waiting to happen. Son already has a track record with poor decision-making about cars. And he is living under your roof. So you do have some indirect responsibility, even though son is an adult. If you were the mover beyond the contract about the car, you were set up from the beginning, with your son. This was ripe for triangulation. In my own experience with my son, triangles are extremely problematic.
I think your own interest is to back out of this. Given it's not your car, and given your son is unlikely to change based upon anything you do, I think you could back out. Unless there is clear danger or abuse, it's really not your business. I think you may be trying to control things where there is no chance of doing so, (like over a car that's not yours). It's giving your son (and daughter) ways to act out towards you.
Backing out of this would be either giving the car back (but then there would be the problem with rides to work), or your backing out of the oversight function. I can see either one of these happening. The important thing would be that you just choose not to be part of any conflict. It's strategic. You just fold. You could let grandfather decide. Tell him, I can't guarantee that the car is being safely driven, or maintained. In fact, it's not. And tell him, if you want son to still have the car you need to understand that I am not able to take responsibility for it. And let him decide. And you back out.
Who wouldn't get offended when mistreated. But you can choose to back off, or to not enter into things, if you choose.
We are no longer responsible to get our kids to learn. They are adults, now. At the same time I believe we are responsible to set moral examples, and to have bottom lines. I think the most important principle here is how your children respect you, to your face. They are entitled to feel about you in whatever way they wish. But to your face to disrespect you, to insult you, to undermine you, NO. At the same time you are responsible to ensure this does not happen, to the extent you can. Part of that is to be very, very careful to not enter into transactions with them that will erupt, or to minimize these if they do arise.
The saying, pick your battles, comes to mind.
On the face of it, it looks like your son takes advantage of ambiguity and inconsistency; that it's his power place over you. To him the dashes between the dotted lines are like entrances. But I wonder if it's something else, too, that he gets anxious when things aren't clear cut. He could also experience you as picking fights. He bucks at the control. To me, all of these things are basic human quantities. They are not serious. He's a young guy wanting to control the circumstances of his life. When he's at home with his parents, and it irks him.
Gosh. I would hate to see you have to take son to work every day. I think this would be entering into another conflictual situation, kind of like daughter and the therapist.
Backing out of this eliminates the ambiguity. You're not in it anymore. You've relinquished your role. You cede. There's nothing to fight back against. Son can work it out directly with his grandfather. I think that's to your advantage in many ways.