Wife has horse. Horse has foundered. So, horse is put in small pen we make close to the house, so he can be recover. Not in big pasture any more. Gets fed pellets, once a day. Has plenty water, but no grass, no hay, cause he needs to lose weight, or die!
Sheriff (deputy) visits. Has gotten complaint we are mistreating horse. We explain, vet says do this, or horse dies. Deputy is polite, says he has to respond to all calls.
End of the week, different deputy shows up. Same story. Next week, repeat. After about a month, we start seeing the same deputy again. Seems there is a lady that drives by regularly, and sees the poor horse penned up, with no food (no bale of fodder), and calls sheriff. Wife is, by this time, ready to chew nails and spit rust. Keeps a lid on it, is polite to deputy (who is about as old as our kids, or looks like it anyway
).
The tell us they know the horse is ok, and the calls are a pain, but they have to check. We ask, can one of you guys talk to this gal and set her straight? They say, they'll try, meanwhile, they don't get all hot about her calls, cause they know there's no real problem. Wife asks about "filing false report" and they say they will explain that to the gal.
Don't see deputy for a couple weeks, and by this time, horse is better, and goes back to pasture. No more visits.
In your case, relax and enjoy it. As long as the sheriff doesn't come "visit" with the SWAT team, (and when they know what's going on, they won't). Have a little fun with it. You're legal. You know it. They know it. Say Hi when they come to visit. Offer coffee, offer to shoot with them, etc.
You can talk to your neighbor, but don't be confrontational. Nothing to gain there, and you don't want him to feel threatened. Maybe he's worried his adult child will get in trouble with you (parole violation?) Maybe he's just a curmudgeon who can't let anyone else enjoy themselves. Doesn't matter. You just keep cool.
Like was said, keep a log of how many times, and what complaint, and when you have a stack of them, go see the sheriff, and seewhat they feel is the best course of action. Heck, by then, they ought to know you pretty good.
You could go see a lawyer, but I wouldn't bother, not now, at least. Just shoot every day, enjoy the deputy's visit, make a log, who, when, how long the stay, why they came. Then with a stack of 15-20 ( or more?), go see the Sheriff. See the man himself, make appointment if you must.
Say something like, Hey, I like visitin' with your boys (and girls?) but seems to me that they could be doing something more important for the county.
There is a line (sometimes legally defined) for public nuisance, for filing false reports, etc. Have documentation to show them, and there's a fair chance they will file their own complaint on this guy, you might not have to.