Perhaps you could approach the farmer for permission to catch the kids (on film) that are doing the damage to his fields because it is also affecting you and that you will both ultimately enjoy the quiet as you are a bow hunter.
You have then told him that you are a hunter, concerned for each of your welfare, and HAVE NOT asked for permission to hunt (at this time).
Following permission to catch the kids and obtaining the photographic proof, take the evidence to him and then see if the conditions are ripe for asking for permission to hunt his place.
You will have done each of you a favor, you will have had access to his land in a "sporting" endeavor (what could be more sporting than catching humans on film without being seen yourself!) and in the end done him a favor if they are in fact tearing up his place. You will have been able to scout his lands and if, that is if you are granted permission to hunt, you are well on your way to the goal you seek.
Also, be prepared for "No". It happens. Don't fret. At least it will be quieter. Like I said, it is a momentary time dependent set back...difficult to await its passing when you are young, but in time it will pass or you will do something to affect a change.
If you get permission to film, catch the kids, or get permission to hunt come back and let us know.
Good luck to you.
BTW: We were target shooting at my place last Saturday morning, about 50 rounds into the morning one gun jambed (misfeed), when we were fixing the problem, a doe came to the rear end of the field in which we were shooting and started snorting at us. Stupid deer...who would a thunk it, rifle and pistol fire is a deer attractant!