Who is at fault if you are driving on a roadway and a parked car pulls into your lane?

A "parked" car will not pull into anything because it is parked.

Ok, not a parked car, but a car waiting in a private drive to get out into the roadway. No signals for the car in the private drive to proceed. The light is red, you wait for the car in the private drive to get out into the eastbound lane in front of you, because that is what they are signaling to do. But when light turns green, the car in the private drive is talking on cell phone and does not proceed or indicate they intend to proceed. The cars behind you are honking for you to proceed, and you do proceed, and the car from the private drive bolts out in front of you and tries to get in WESTBOUND lane (did not indicate this by any action at all) They bolt out so fast in front of you, that you hit them in the rear quarter panel. The car who pulled out in front of you, from a private drive and you hit, leaves the scene of the accident after exchanging ins info, even though you indicate that you are calling the police. And the police come after they leave, and determine it is not your fault, it is the fault of the person pulling out of the private drive. BUT both my ins company and their ins say it is my fault! I threaten to get a lawyer and demand to have this person's phone records produced, showing that they were talking on the phone and they were distracted. (which my ins co was going to do initially, but the other person refused to have cell phone records released) So my ins company takes back their claim that I am liable and they are doing further investigating. It has been over a month now, and my ins company still has not determined liability, after initially claiming I was liable. How long do they have to determine liability? My car has $1500.00+ dollars in damage and I have personal injury, and the vehicle that pulled out in front of me had $450.00 dollars in damage, and no personal injury. Wouldn't it be in the best interest of my ins company to do a very thorough investigation of the accident, taking pictures of the scene etc. Instead of just going with the other person's ins decision that I was liable? Seems to me that my ins company would fight for me, instead they just concede to the other person's ins very quickly. Even though the police report says I AM NOT At Fault AND SHE IS?