How do you decide who's at fault in an accident?

Answer:

• In the UK - determining who is legally at fault depends to a degree on the type of accident that has occurred. For example - in a RTA the Road Traffic Act and Highway code are influential in deciding who has made a driving error. In an accident at work there are regulations for manual handling and keeping a work environment safe. For examples on showing legal fault for different two different types of RTA and work accidents see the related links entitled: "car accident claim", "motorbike accident claims" and "accident at work claim".

Answer

Here's a link for advice on determining who is at fault in a car accident.

Besides the website recommended above, you should consider point-of-impact, whether the alley is one way or two way, and what a reasonably prudent driver would be expected to do in this situation.
In your case, the point-of-impact is very telling. It's one thing to hit the rear corner of a car backing down an alley, but it's quite another to hit that car on a door. Your neighbor, even while backing, probably had the greater duty since you clearly had control of the roadway.
If there's any comparative negligence on your part, it would be minimal unless the alley is one way and statutes specifically prohibit backing in such a location. A statute of this type could be used as a defense for your neighbor because the statute would have been created with just this scenario in mind (i.e., don't back down a one way alley because most people wouldn't think to look more than once in that direction).
Another thing to consider: Your neighbor basically struck the middle of your car. She has a duty to watch for oncoming traffic. Clearly she wasn't watching. Now, suppose that had been a person? What would her defense be?  

Answer

Fault is determined partially by the laws of your state.
Contributory Negligence Comparative Negligence
Under which of these systems does your state operate.
In one...the person who is 51% at fault will pay for all damage. In the other a percentage of blame is assigned and each pays that percent of the others damage.
It could also be a NO-Fault state in which your own company pay regardless of who is at fault.
General rule of thumb....the person with control of the "roadway" has right of movement. Anyone entering the roadway must yield to the ongoing traffic.
A smart attorney could argue a case that alley's are not roadways.