My question involves a traffic ticket from the state of: Michigan

I was turning left out if a parking lot, intending to go east. The traffic was very backed up, and stopped at a red light. The driver in the far right lane stopped just prior to the driveway allowing me to exit. Next, the driver in the adjacent lane stopped to let me out. I eased in to the road, checking to make sure that eastbound traffic was clear, and as I proceeded to turn left, was hit by my front driver side by a car that came barreling down the center turn lane. The other car spun out into the open eastbound lanes. I was given the ticket even though the other car had entered the turn lane too early and was passing the other stopped cars. Of course because of all the stopped cars I couldn't see the other car coming. I understand traffic in the road has the right of way, but is that so even if the car was illegally using the center lane? The cop was very mean to me and not to the other driver. Wondering if I should fight this in court.