Can I fight this ticket & insurance co? Even if mutually at fault, other driver deserves some blame but report leans to me only.

I was turning left from a parking lot across one lane of northbound traffic. Two northbound cars had stopped for the red light and left room for me to inch out and check for traffic approaching in the south bound lanes. The other vehicle tried to catch the green turn arrow by passing the two stopped cars on the left using the turn only lane. This lane turned into a diagonal yellow painted median and eventually became the left turn only lane at the intersection. Accident occurred in the pained median. She improperly passed using a turn lane and violated the painted median that lead to the crash yet I was cited for not yielding. I looked both ways and slowly turned out, she flew up from around the cars as I was already beginning to turn.