You are in a difficult situation, but you both need some time and space to calm down. Don't contact her just yet, but after maybe a week you will have gathered your thoughts and can write to her. Just say you are sorry things went so badly wrong and you didn't mean to upset anyone. Just make it clear you love her and the children, and are here for her whenever she needs you. Say that you hope to hear from her soon. Then let it go. Don't start analysing the car situation, what happened or why it happened. Don't bring it up. If she ever wants to discuss it with you then fair enough, but do so in a calm way.
I would suggest always trying to keep an air of calmness whenever you speak or see her. If she starts getting worked up do not try to answer back and argue the toss because it will end up in a full blown argument. Watch out for her mood swings and if she's aggressive then just shut it down, say 'we'll talk later' and leave. That may leave her fuming but neither of you will say things you later regret. Always send a text afterwards, saying you love her and are here for her, but can't cope with arguments.
She probably won't go too long without contact if she needs your help, but after another week maybe send a text with the same wording so she knows you're waiting for her to get in touch.
Remember she probably needs you more than you need her, so don't be a doormat. Let her make some effort to keep the relationship going. Keep calm because she is exhibiting enough emotion for both of you.
Hope that's helpful, it's how I see a way forward.