First, better buy an orange hat or three. It shows an innocent intent.
Second, no matter what you do, this is going to cost you, and paying the fine could end up being the cheapest option.
My larger concern would be if/how such a conviction might have any bearing on your continued firearms ownership rights, and yes, a bow is considered a firearm.
Then, this is not just between you, the CO, and some Judge.
There is also the Prosecutor.
You could simply pay the fine, which also involves a mandatory 'guilty' plea and conviction on your record; or you could contact the Prosecutor and try to negotiate the charge down to something that does not imply a conviction on terms that could impair your firearms rights or hunting privileges, perhaps to something like misdemeanor disorderly conduct. Even if the fine is greater, it could end up being less of a hassle in the end. Explain that you have no qualms with paying a/the fine, but that you believe the circumstances were predatory and arbitrary, and that you are more concerned about any subsequent implications on your gun rights and hunting privilege (and especially those of your son) under such conditions where no victimization could possibly be present. I would suggest that pleading to a lesser and more generic charge would be preferable, no matter what the monetary cost of the consequent fine. Simply being put on your best behavior for a year is also an option.
Make it clear that if the original charges stand, there will be a vigorous and well publicized defense. If they stonewall you, have your Lawyer get in touch with the local media immediately, before some Judge can issue any gag orders. Local TV stations love this stuff, it sells a lot of underarm deodorant, etc., for their advertisers.
While this might seem financially counterproductive, finding a lawyer who has a positive relationship with the prosecutor could be cheap at twice the price. Let the Lawyer do your talking with the Prosecutor. Do this right and you could spare yourself and your Son from the influence of some capricious or biased judge, as well as recorded/archived testimony and/or adjudications on a court transcript. I would also seek to have the records of any convictions naming your Son be sealed or even immediately expunged, whatever he's charged with he was in the presence of and under the direct authority of a responsible parent, who should rightly bear all responsibility.
Prosecuting children for the acts of their responsible adults does not set a good legal precedent, and court officers who stand for election do not need such precedents on their records. Don't be afraid to bend them over backward where their political careers are involved, but having your Lawyer do it instead is way more preferable.
Money and pride are not the issues here, you need to ensure that you and your Son are not perpetually encumbered by arbitrary and/or mandatory legal encumbrances. Once the summons has been issued, there's going to be a cash outlay no matter how you play this; so you may as well get your money's worth, and have things end on a more favorable note.
In a recent legal incident involving a close relative, we (we are a family) followed this course, Although a court appearance and a plea of 'no contest' were required, the charges were far more favorable (no mention in the papers), there was no sentence involved (there could have been), and the costs for court fees, lawyer fees, and fine (about $1000 all inclusive) were far preferable to visiting a relative in some correctional facility. Cheap at twice the price, I'd say...
This may not go over well with the CO, they can get ornery, and this guy already knows where you live...
If they try anything like intimidation, etc., you get it on record (with the Prosecutor's office, via your lawyer) that you believe your are being intimidated and harassed. If that doesn't do the trick, charge the CO formally with felony intimidation and police harassment, as well as threatening civil suit. They do it all for their retirement, and they will usually back off when the alternative involves having to face a legitimate criminal charge.
But most of all, clear the air about not being willing to be some CO's clown/patsy. Don't be afraid to whip out your cellphone on the spot and in a loud and frightened voice, tell them that you are unarmed and currently being threatened by an armed assailant.
After all it's the truth!
Greg