Sorry to hear.
Valuable info in both of twsas's threads... some not applicable to your situation, since his was new and yours is used.
My comments:
1. HOPE it is totaled. It looks like the A and B pillars are tweaked, as is the front drive components. twsas had a new car (with a higher value) and it was totaled- yours will cost the same to repair so it will likey be totaled.
2. DO NOT WAIT for the other party to file claims. YOU drive the issue. Call their insurance, file the claim. TAKE METICULOUS NOTES. Date, time, names. Do not underestimate the value of this. In the event of any issues, your ability to whip out a letter saying "I spoke to X on Y and they said Z" will put them on notice that they cannot afford to not pay careful attention.
3. Your big problem will be coming up with a value for your loss. I would find every CPO car in the USA which matches your car (model, options) and print out that page. TODAY. You can then make adjustments based on mileage. They will try to use an independent company and WILL lowball the process- your argument must be that ONLY a comparison to "CPO'd" cars is valid. Any data they provide for a "non-CPO" is not acceptable. Be prepared for a fight.
4. Rent a full sized 4 door. It doesn't matter what your policy 'covers' or their policy 'covers'. Be aware that once they present an offer to settle a total- not an acceptable offer, but any offer- they stop paying for the car (IIRC)
5. Understand the relationship between you, the other driver, and the insurance companies: The other driver hit you and is at fault. The are LIABLE for your LOSSES. Importantly YOUR losses are not defined by HIS policy. Think about this: his coverage, or their internal procedures or what they allow or how they do things- all of these are of no concern to you. At the end of the day, the other driver OWES you for what he did- the other driver entered a contract with a third party insurance company who has agreed to cover his liability in the event he causes an accident. If the other insurance doesn't want to pay, fine- you'll sue the driver. (Note: Nobody wants to sue- it is a PITA, and can be expensive. Luckily there is small claims which would likely cover the difference between what they cover and what you are out of pocket- but just understanding the distinction and being comfortable with the terminology and carrying yourself appropriately with the adjuster will get you miles ahead.)
6. Your insurance sounds like dciks. The should not be demanding the deductible up front. The could also be acting on your behalf with this- what I see is generally all insurers- both the at fault party's and the other- acting in the best interests of BOTH companies: they want this done quick, they want ot done cheap, they know one day they pay, one day the other pays- they have no incentive to go to bat for you. Case in point is car rental: they could say "Rent what you need, no luxury but 4 door is fine- we'll make the other side cover it". Isn't
that a fantasy?
7. (edit) Finally do not ask them 'what do I do next?'...neither of them. The are not there to help you. If telegraph your uncertainty to them they will exploit this- it will make them much less likely to concede to your demands... this is hard to do, you are starting now.
Good Luck
Keep us posted
A