Not knowing anything about your case makes it hard for us to answer that question but it is your decision to go to trial and fight or take the offer of infractions. Infractions generally are good offers but you should also think about the cost of going to trial versus taking an infraction and getting done with it.
A private lawyer offers you oftentimes more personalized attention on your case but the facts are the facts. A reduction to an infraction may be an appropriate resolution depending on the facts of your case and the particulars.
First you have to specify what charges. In general, client is the one that will decide to take the offer or not as only client will suffer the consequences of that decision.
In your situation, if you plead guilty to the charge that is infraction, you would pay the fine but that would be in your record. However, if that is not what you want to do and wish to proceed to trial, you need to communicate the matter and clearly state your decision to your attorney.
If you are convinced of your innocence, you should fight this case all the way, especially if you believe you have the evidence which establishes your innocence. However you should ensure your evidence is of an exculpatory nature and, to determine that, it should be reviewed carefully by the lawyer of your choice.
Realistically, if you wish to fight this case through trial, you need to retain an attorney who is aware of that and who will agree to try the matter. Your first step should be to consult with some attorneys to secure a consensus opinion of your chances of success. Obviously neither myself or anyone else can give you our opinion on your best course of action without a comprehensive review of your case.
An infraction means no jail time and it rarely goes on your record. Better consider how strong your defenses are.
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An infraction is usually a great offer and, similar to a traffic ticket, does not affect your future or clean record. It is a fine-only offense, does not have to be reported on employment applications that ask for felony or misdemeanor convictions, and you would not even be placed on informal probation.
How strong is your case? You don't want to roll the dice and lose, then end up with a misdemeanor which WILL affect your clean record. If you have a great case go for it. If it means that much to you go for it. Just be aware that you could end up getting a worse result than the infraction.