The only issue for your career as a teacher would be if you refused to pay, it went to county court and they won an order for you to pay Even then, it would only be an issue if payment was not made within 28 days.
Having said that, If your husband admits liability and asks to negotiate with Admiral then they will probably be content to do that.
You are right, their policy says they can go after either the policy holder OR the driver to recover their costs.
That means they will go after the one who is most likely to be able to pay up. So if you are a teacher on, say £40,000 a year, and your husband is a caretaker on £12,000 then it would make sense for them to want to try to make you pay.
If you think about it, you took out the policy and agreed to the terms that included being liable for costs if drink driving was involved. (but I doubt you read them.... your choice) All your husband did was to be placed as a named driver on YOUR policy. Did you ask him to read the terms of the insurance before he drove? I doubt it. That is why common sense says your husband is responsible for the cost of the accident, but you are the one who had the chance to read the conditions and back out if you disagreed. Admiral therefore feel that you can be held liable for the named driver on your policy causing them a loss.
I would think it is common for a rental car to be hired for 32 days. The car was eventually a write off, but they would have to get it inspected, estimates submitted and then a replacement vehicle being sought after the total loss was declared. BUT it should be like for like, not a bite car that is better than the car written off. It is quite reasonable to ask for the details of the hire car.
I doubt it will do much good to challenge the engineers report, unless you think the damage that was witnessed was way too minor to justify it being written off. You would have to pay for another report and bear the cost of that.
It is reasonable to query the personal injury element. Does your husband say that anyone appeared to be injured at the time (but things like whiplash can develop a couple of says later) You could ask that the medical report be anonymised to prevent personal details being improperly disclosed and demand that they tell you what was done to minimise the costs to them.... and subsequently to you!
One last thing, did they write to you or your husband, asking you to sign an indemnity for Admiral to negotiate the settlement? If so, was it signed and returned?