First, based upon what you described as your property situation and backstop, you really do need to construct a better backstop. What you are describing is really a little shakey to me.
Warning: Unpopular opinion incoming...
I know the kind of neighbor you are referring to.
While I applaud those that immediately have "Take them shooting" as an answer for everything, this is not a "Catch-All" answer.
There are simply people that do not want to shoot. Likewise, there are people that I have no desire to have anywhere on my property or handling any of my property.
A real good barometer of that is if that person has:
A.) Ever come banging on my door making demands the way you described.
B.) Ever CALLED THE POLICE... especially several times.
I see a person who wants to get their way-- the law be damned. As I see it, the instant the LEO's told her that you were in your rights and it was "safe," there should not have been another call regarding that. Any more calls seems to be a strong-arm attempt at harassment.
This is NOT a person you are going to be "friends" with (or at least I won't be.)
Moreover, I am not about to invite a person onto my property that has a beef with me. That opens me up to a whole new world of potential liability. I do not trust this person NOT to decide that if they can't make you stop, they will ruin you with an injury lawsuit-- thereby forcing you to sell and move.
I have a few hundred acres of woodlands. Routinely, we have people attempting to come in uninvited. I have seen with my own eyes what some people are capable of.
One of our landowner neighbors had someone sneek onto their land during a party. She was driving her car while drunk. Naturally, she ran into the ditch and got stuck. She got another drunk friend to pull her car out of the ditch with his truck-- in the process, they broke her axle.
That next Monday, she sued the LANDOWNER for damages to her car!!!
Sure, it went nowhere, but the landowner had to hire a lawyer to deal with the mess.
Consider what you open yourself up for if you go the "take her shooting" route.
Me? Sometimes you have to realize that not everyone is going to like you, and not everyone is going to be accepting of your interests-- ESPECIALLY a person used to dictating their desires to others and accenting it with calls to LEO's.
Some people may try to paint all this as me being an "Internet Commando" or otherwise being short-sighted. To those people, I say only this: YOU haven't had to pay for my liability umbrella insurance policy for the last 15 years. It is people like this that cost me money every year.
-- John