if you felt not fair and confident you saw a green light, then you should go to court to argure. At least you could know why the police felt you had the fault. I believe it will benifit you and your child. A good driving habit is more important than a case. I belelive the plice did not give your license back because he saw you had a kid in the car. on the other hand , tell you insurance company what you remember, and to see what it will do.
If you have good driving record, that will help you in the court as well.