You can go to your first court date and request a trial. This will be a trial in front of a judge, not a jury. The officer will testify, then you will have a chance to tell your story; you should also take your mother along as a witness.
I would strongly suggest that you invest twenty bucks in a copy of Fight Your Ticket and Win in California, published by Nolo Press. It's a very good guide to traffic court.
I have heard great things about that pamphlet as well. I agree with what Mr. Marshall said above and wanted to add that you should also bring your mother to court as a witness to testify on your behalf.