I'm not one to have a bone with others or their animals- in the case of an accident or some such. But per a THREAT of a dog being sent on my property, I'd make sure it's legal to shoot (seriously, b/c what if something happens & you can't just go out there nicely & remove the dog?), file her threat with the police & post 'No Trespassing' signs up (some places require this to legally protect your property, etc.), then I would inform them that you've filed her threat with the police & that they said you're legally allowed to protect your livestock (if so) & leave it at that.
My mom lives in an area where people dump dogs all the time, she's collected a small group of dogs from this & they're great dogs that protect her property well, but she still reserves the right to shoot one if it goes on a rampage, this applies to other predators too (2 Christmases ago we had a covert coyote attack on the horses).
She also has a neighbor who was just a B, for no known reason she would antagonize her dogs- including bringing her dog down on her 4-wheeler, stopping at the end of mom's drive & letting the dog down to stir things up. She would also proceed to drive back & forth in front of the property with her dog running which would of course, cross onto the property & get a good run at the horses, or run up the drive. Mom made a point to inform her she has the right to shoot that dog if it steps foot on her property again & most certainly will if she feels it's threatening her horses again, or her dogs! This pretty much stopped this woman from doing it.
It's completely uncalled for, this type of behavior, it's worse when the threatened parties do nothing to firm to stop it- legally it also muddies the waters. What if you sit on your hands, do nothing in return to the treat & she sends the dog in at night, or intentionally when no one's home? What if this dog ravages your animals?? Sometimes by doing nothing can reduce your ability to claim harm done. Informing her of your rights, making a formal complaint about the threat, THEN if anything happens, allows you to claim harm done, and/or protect if necessary.
But I would MOST CERTAINLY inform them in no uncertain terms that you won't be allowing them to store anything on your property in the future (remove anything that's currently there)- as this opens the door for them to enter your property even if you're not there & can again, muddy the water if she just happened to bring her dog with her sometime... if you know what I mean. I would also make sure they understand they can now look elsewhere for any assistance with their animals, period.
IMO, life's too short to deal with crap like this & if you've been good neighbors & that's her return to you, I would cut all ties & make sure they realize I'm serious about it, end of story.