i feel your pain, to steal a line from someone else....that said, state laws vary when determining "fault" in an accident. In california, it's called "comparative negligence", and it simply means in MOST accidents, there is a certain degree on fault that lies with BOTH parties in the accident. It may be as "lopsided" as one party being 90% at fault, and the "innocent" driver 10% at fault. Keep in mind it is the insurance companies that will determine this as far as paying claims goes. And, yes, the insurance company can say you were say, 20% at fault, even if the other driver was cited for a traffic violation and you were not. But of course, you are asking "what type of lawyer you should contact", and my answer to that is one who specializes in insurance claims, (since you said there were no injuries). And sure, you can sue the other party, but that can (and probably will) cost you big bucks, with no guarantee of winning a settlement. Yes, it sounds like i'm being very pessimistic (which i am), but the reality is an attorney will tell you much the same thing. There is some good news, though. If the accident happened while the other driver was insured, it doesn't matter if they cancel or not---they may/will still have to pay on the claim if a court says they must. A good claims att'y will no doubt write a letter to the insurance company explaining as much, and this often will do the trick---the insurance companies know if they don't pay, they'll be forced into court and their cost will also rise dramatically. It sounds like you have a good case---but in all honesty, we are only getting your version, not to say you aren't being truthful, just that there are two sides to every argument/story/accident account.
hope i helped a little, and good luck.
