To not accept this was an accident

The more you've said, OP, the worse it sounds.
He's inconsiderate and arrogant (driving toward people). He doesn't take any responsibility for injuring people and doesn't seem to care if he has (the incident with both you and the broken arm).
I'm not sure that being with him is safe for you or your children.

Your updates are incredibly worrying.

Are you scared of your husband?

I agree. His refusal to take any responsibility is chilling.
See the GP.
You need to tell someone.
He is injuring his family and takes no responsibility.
This is red flag and dangerous territory.
Stop trying to convince yourself that this is normal.
Its not.

Has anyone ever stood on the zebra crossing infront of the car and waited for him to stop. What happens if the person doesn’t cross in time

I would be telling him you can’t do anything because of your shoulder so he now has to make dinner, drive you to A&E, wait for you there, feeding the metre each hour.

Until he learns that all this time saving actually wastes his time and money he will keep on doing it.

This update makes me think these “accidents” are definitely deliberate.
Especially when he is more concerned about the narrative being accident rather than asking how you are feeling or apologising

Taking your young child into a teenage area of the park is also deliberate. What did he think was going to happen?

I would be logging these “accidents” and your mistrust of him being in charge of dc and all the incidents that you can remember at the doctors

If you do decide to leave and protect yourself and dc then he might get supervised visits and not be left alone with dc

Just read your updates. How old is this man? He’s acting like an impatient and impetuous child.
To be honest, if it was me this would be ultimatum time. Either he makes a sustained effort to be less self-centred and careless or the relationship isn’t going to work out.

He sounds like me when I was young. Chronically careless. In his own little world and so busy doing things his own way / at his own convenience that he isn’t thinking of the collateral damage.

He needs to feel the consequences, that’s the only thing that will make him change.
I don’t mean to punish or shame him, that will cause bad feeling.

Try stepping back, hand over more responsibility and never ever ‘save’ the situation if it’s going to go pear shaped. Was it he who took your child to the hospital and all further appointments when he broke his arm? I hope so.

Eventually being careless will become so inconvenient / embarrassing / stressful he will have to make more effort and take more care.

OP I don’t think you have answered whether he hurts himself too? If not, then I would be very worried that there is unconscious and possibly dangerous stuff going on. If he does injure himself, then yes- I was thinking dispraxia. But I would definitely have a serious talk with him one way or another.

Yikes. Your update makes your husband's behaviour alarming. This is someone who doesn't care about anyone else or the consequences. If you don't get out of his way, tough on you.
Contrary to my last post, your children need to never be left alone with him. He's a safeguarding risk.

He is a dangerous driver and should give up driving. He will kill someone soon.
This is another red flag.

Shutting the boot on someone's head is NOT an accident, it is deliberate.

Not seeing that a child is seriously hurt and is in pain is NOT an accident and is also deliberate.

These are only two examples of his behaviour. His actions are putting your child and yourself in danger. He could have killed you by closing the boot. Can you not see all this is very dangerous and escalating?

His attitude is another red flag: Not taking any responsibility and blaming others.

Please take action to protect your child, you and other people.

Ok, he’s either dangerously aggressive or has some extreme phobia about stalling the car.

none of this is okay

I think it’s more than dickish. He’s arrogant, contemptuous, bullying, threatening and dangerous.

That rolling the car towards pedestrians is just dickish. No excuse for that.

I know he's not doing it on purpose but I would find it appallingly stressful living with a man like this. I'd be constantly on edge.

Is he caring in other ways and a good husband OP?

The way he reacts after these accidents is what would give me cause for concern. One can be clumsy and acknowledge it and still be able to check if the injured person is ok. Reminds me of my ds when he 6 or 7 - everything was ‘it’s not my fault, I didn’t do it, it was an accident’ Thankfully he is now 11 and takes accountability more than your dh does by the sound of it

I don’t know.
That’s why I’ve said she should speak to him about it.

Because this is her husband we’re talking about. Not yours.

I slammed the boot on my 5yr old's head once, very hard. Obviously an accident and I was terrified but fortunately she was fine. So it could be an accident but sounds like there are wider issues.

Terrified? Or just doesn't want to?

I assure you in my ex's case he wasn't terrified, he just didn't want the blame/responsibility and would minimise at every step (unless it was my mistake). And yes, he also took care of his things, but ruined mine regularly.

That he's not apologised means he's a bit of a prick tbh.

But you'd be sorry about it though? Kicking yourself for not taking more care? Unlike OP's DH

Sounds like he might be dyspraxic.

It's hard to say. My ex seemed to completely destroy a lot of things by "accident", but they were only ever my things (especially favourite, irreplaceable things). He'd also never take steps to mitigate these "accidents", like using his own plates or buying cheap ones from Sainsburys (he'd rather break my expensive ones that are no longer made). It took me almost a decade to realise that it's not actually possible to be as accident prone as this with only one person's belongings.

It sounds like your DH is immensley impatient, thoughtless and a man child (not taking action when he"s caused an accident, like your toddler breaking their arm). I'd actually take this seriously, and if he doesn't start to change, consider leaving. I'd start with a conversation with him, saying his impatience is hurting everyone in the family, and he needs to change. He needs to take a moment to think about consequences and alter his actions accordingly. And when an accident does happen, he needs to take respomsibility, own up, apologise and do whatever else is necessary (like taking a child to a hospital). If he can't do this on his own, he needs to seek an experience therapist to teach him life and coping skills.

Yes, but, knowing that he's clumsy, my son takes extra care not to hurt other people.

That's the difference I'm talking about - not how clumsy you are, but how you deal with that and how it impacts other people.

Injuring other people because you can't be bothered to take a moment isn't acceptable - accidentally sometimes, perhaps, but a caring person would be very apologetic, and would be much more careful next time. My son would be horrified if he shut the boot on my head. He wouldn't brush injuring me accidentally off as though it was nothing.