What did they cite you for? Did you hit another vehicle or do property damage? Perhaps it's for failure to yield, failure to stop at a traffic control device? If you want to fight the citation you need to focus on the cause for the citation and show that you didn't commit the violation.
We need more info in order to answer this question.
It would be best if you did not take the baby or if you took a friend with you who could watch the baby when you're actually in front of the judge.
BTW I'm a retired police officer.
I have seen the judge both lower a fine and dismiss a citation. Perhaps I can help you know how to word your situation to the judge if I knew more details.
After your edit: Yep, this is illegal. The Sheriff's secretary had this happen to her and she was cited. I have difficulty understanding it, too.
You were probably in the parking strip or on the side of the road not intended for traffic use. (tho it may actually be used)
The fact that the driver of the van left the scene is a different issue. When found he'll be cited for hit and run but his turn was legal.
I suggest that you go to your local police precinct and ask the desk officer or a traffic officer explain this to you so that you can speak with knowledge in court. I suggest that it's possible that if you're able to show the judge you now understand that he will reduce the fine or perhaps even dismiss it. Just depends on the judge and the court philosophy.
In our county, a deputy district attorney is not assigned to traffic court. Otherwise Ina's suggestion would be a good idea. I suggest that she was able to testify because the case had gone beyond traffic court.
I suggest that you plead ignorance in court. If you were planning to turn right, you could argue that you were closest to the curb in preparation for a right turn.