Oh Nutty,
I'm so glad you have your children with you, your family and SI, and so sorry your H has turned into a monster and is hurting you continually.
In the UK, do they consider the car his, even if you are both still M? Like another poster said, it seems the car would technically be both of yours, and in the event of a D, it is half yours.
Can you ask him for his new car in order to get the children to school, the doctor, etc.? Make him believe it is temporary, and remind him he can use OW's car in the mean time? Then, have the locks changed and don't give it back. When you get D, you'll most likely have to sell it and give him 1/2, or perhaps you can keep it, giving him something else for his half.
If you can't get the car, does anyone have a car for you to borrow?
Regarding the letter stating he had an A: if you absolutely need some sort of proof to get a D on the grounds of A, then I would suggest you not tell him anything about D, and especially that you need a letter in order to do it. If he knows you are pursuing D, and you need a letter stating he had an A, he will most certainly not write it.
Find another way to get him to admit to the D in writing. If he won't, at least get copies of everything he and OW have posted on FB, and other places that reference their relationship and cohabitating.
I am so sorry for the loss of your precious little one. That alone is devastating.
OW has not taken your life. She has just taken your monster of a H, and set some serious changes in motion. You still have your life, it will just look a little different from now on, but it is still your life.
When your think of your loving husband, remember what you said about his life spiraling out of control after his dad's death. He was not a stable man then, he said you were the stable one and you saved him. So now he is spiraling out of control again, and it is not because of the loss of the baby, it is because he was never stable. He sounds like a disaster waiting to happen, and although it hurts right now, it would have hurt in 5 years, or 10 years, or whenever he decided to throw in the towel on being a devoted, reliable husband.
You are the stable one. You will put your life together again, and be happy again.
Hugs for you, (((((nutty)))))
HBH