I dared to tell her that if she'd checked the mirror before hard braking she might have realised what might happen. Mrs still denies that she made a mistake.
What do you think?
That You're a brave man

The main fault is with the driver behind who should ensure they are able to stop, whatever unexpected event occurred. And insurers would typically regard them as to blame ,but as the Insurance industry know they will win some and lose some it may not be worth their while spending too much effort apportioning blame.
I'd say a driver should be constantly aware of traffic all around them and therefore already aware in good time if there is a car too close behind . This gives you time to protect yourself by braking sooner and more gently,or to justify not stopping suddenly on an amber. Or if its a persistent twit ,time to move out of their way.
Safer driving is not just about not making your own mistakes . With good hazard perception you can anticipate when others might make mistakes and protect yourself from them. Its a bit like the proverbial grave stone epitaph " He was in the right , but he is still right here"
But saying you should look in the mirror before heavy braking is to some extent leaving it too late. Having to brake hard is sometimes a result of the drivers own poor hazard perception and late reaction. If you have no option but to stop in a hurry you may not have time to look in the mirror. Amber lights is a bit of an exception. You often have time to check mirror and decide if its safe to stop.If its not safe the light will still be amber and its legal to carry on. If its a bit tight and you havnt time to check, its usually best to assume its not safe and carry on, as the light will still be amber (wont it . If its now red you have no excuse for your tardiness and should be ashamed of yourself.)
So I dare say your wifes hazard perception could ,like most of us ,do with some improvement. (I dare say it, but will you

)