I think the dream is reflecting with symbols the way you feel inside of you emotionally . It was saying that inside you feel hurt, ignored and devastated. (Jessica ignored you)..........She (the other person, whose fault it was ) is probably Jess.
Everyone was coming to her aid. Everyone cared only about her........
She made a spectacle of herself.....in a way.
The end of the dream I think may have to do with her again, asking for Help and forgiveness.
The car and dust on it, is symbolic of you, and how you feel (your consciousness is the car you use each day to transport yourself)
The writing on it, was pleading, to you to understand how sorry she is, and wants your forgiveness, (but not on this level), from the higher self.
This was a message from the spiritual realm in which your dreaming self, met up with hers........
On this level she's still the same (nasty, angry, hurt & bitter)about her life.
But on the spiritual level she is a "whole" soul and understands the wrongs she has done.
The two merge but the ego on this level doesn't allow for the spiritual self to come out, when egos are THAT strong and defensive.
This then, is her mental illness.
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The dark haired man was symbolically "Mark" dad thinks. not cooperative and not helping at all.
The keypad and pushing the buttons was because of your new "Help" Phone system.
You are crying out for help (emotionally).......
The car turning now into the Prelude instead of the Accord.,is again your own consciousness, and you see in the older car, the older consciousness and "past" Injuries that are responsible for her today's problems. ALL the past events for Jess are causing injury today for you as well as her.
You were being (in the dream) normal - normal driving, normal caring & seeing about your sister....
She jumped into your lane & hit you.....bringing you into all this. And emtionally inside, this is how you feel and your dreams usually will reflect this.