Oh Sergey, I am absolutely devastated for you
I am currently dealing with a non-fault claim on our S5 (much less damage - just front wing, a wheel needing a refurb and a bit of paint on the front bumper) so have some recent experience.
Firstly, you must absolutely notify your insurer ASAP - tonight ideally - it's a notifiable event, even if you intend not to put a claim through them.
Our S5 was hit while parked and unattended, but mercifully the delivery driver involved had a conscience and left his details on the windscreen. The number on that form took us through to the accident management company for that firm. I looked at getting it sorted through them as they were offering to sort equivalent hire car etc, but it quickly became clear they are predominantly aiming at the fleet market in terms of the quality of their repair centres - they just want vehicles back on the road ASAP, and none were Audi approved.
I am now going through my own insurer (Admiral on this car) and it is booked in to a semi-local Audi main dealer who have a bodyshop on site (branch of Harwoods, who previously repaired my wife's Xsara Coupe after another bodyshop left it bent when they did a quick repair on the insurance many years ago without jigging the car first!)
One point of note is that insurance companies will have different acceptable standards of repair (read 20mm of filler!) compared to Audi (more like 2mm) which will result in more panel replacement. You are within your rights to demand it is at least assessed by an Audi approved bodyshop, particularly due to the aluminium construction. Details here:
http://audiapprovedrepair.co.uk/
Worth at least having it assessed - but worth calling to make sure they can deal with aluminium panels as there's several in your area.
The guilty party here needs to return you to the same position you were in before the collision. That means an immaculate 3.7 A8 alternative, or your car made good to your satisfaction. If the car cannot be realistically replaced, talk to your insurer about using your legal cover to check how far you can push for a repair, irrespective of the cost. It might be cheaper for the insurer to write your car off, but if that doesn't put you back to the position you were in before (the owner of a mint D2 3.7) so you can insist on a repair.
Only at that point do you then need to decide whether any quality of repair is going to be acceptable to you - I know how fastidious you are, so finding someone who understands how important it is for the car to be returned to looking like new is key there. If you aren't confident, then accepting that's the end of the road and dealing with the salvage to ensure other cars benefit from all the work you've done is probably the best you can hope for.
Ask yourself this - if you were buying a car today and could buy anything, what would it be? If the answer isn't automatically a D2 3.7 then it's probably not worth the aggravation that'll be involved in trying to deal with it.
Get proper legal advice, whether through your car insurance if you get it, or check your house insurance too
Best wishes
Adrian