I even been in three car accidents.
The first in a taxi which didn't slow for a roundabout and someone pulled out in front of us. This caused significant whiplash which still affects me almost 15 years later.
Second was my fault. Driving too fast on a slick road and I spun it and ended in a ditch. No damage to car and no injury to me because I was braced for the impact.
Third accident was as a passenger in a friend's car at a roundabout waiting to pull out. Friend got ready to go and took her foot off the brake and began to roll forward but realised the gap was too small, so stopped. White van man bumped into the back of us at a crawl. We got out, he said 'I thought you'd gone!' Another knob who didn't use his eyeballs.
At the time it seemed like no damage to the car and we were fine. Next day we both had sore, stiff necks and the car had sustained a fair amount of damage as although the bumper looked fine (they're designed to crumple and spring back), it had damaged the underneath if the car and the boot catch was broken.
This third accident aggravated my first whiplash injury and I do still have problems several years later, costing me a fortune in osteopath fees. It's well known that if you see an impact coming, you brace to protect yourself, if you don't, you have no way of stopping that extreme forward-backward motion as your body stops but your head carries on travelling.
So actually, no, the woman isn't an arsehole and £1500 is probably getting off lightly for your DH tailgating in a large vehicle and not paying attention to vehicles in front. This woman could potentially have long term ligament damage, plus the inconvenience of being without her vehicle while it's off the road and in for repair. Your DH's poor driving behaviour has caused this and he needs to suck it up. It's his fault and nothing - not even her shouting at him or her claim on the insurance - mitigates that I'm afraid.
Deal with the insurance and hope that your DH learns from this that driving too close and intimidating other road users is actually bloody dangerous for other road users and costly for him.
As it stands, the other driver involved is going to be far more inconvenienced than your DH, who is, in fact, the arsehole.