Kid (who's not allowed in my yard) got nipped by my dog (while in my yard) and parents want me to pay!

(In Minnesota) My neighbors have been a bother since I moved in, as the land apparently used to be owned by their grandpa so the kids feel entitled to come and go. We've had issues with boundaries (personal and physical) since day one.

Long story short, I went outside to check on my 6 year old playing to find all 3 of neighbor's kids jumping with her on our trampoline. I told them to go back home, they got off, then their oldest (13) stomped at and made barking sounds at my dog. I said "Don't do that". He then climbed up and rode our small zipline and my dog, who gets nervous and excited, chased and nipped at his leg on the way down.

It's a small scrape. I told them to leave and I put the dog in the house.

Neighbor mom freaks out yelling at us "Why is your dog out?!" etc. and I'm like "Why are your kids playing on my stuff?!?" She says he needs to go to the hospital, she's gonna call the cops, we're gonna pay for this...

So preemptively I called the police to start a report (should have a long time ago) of their kids trespassing on my property.

Today I got a notice to provide my liability insurance for the doctor visit. Ummm, NO. How do I fight this??

Also, what else can I do proactively to guard against them in the future? No trespassing sign? Restraining order?? And before you say "build a fence", I share like 150 ft of side yard up against their backyard and if I had money for a 6 ft privacy fence it'd already be built!

EDIT TO ADD SOME INFO:

The land was sold 10 years ago to previous owners to build on, with the (odd) exception that “grandpa” kept his old shed on the far side of this lot, and access to it anytime. So grandkids considered it “their grandpa’s yard” up until...

When I bought the home 18 months ago we required the old shed be torn down so we have our whole lot and be rid of that strange arrangement.

So this is why it’s such a weird issue to our neighbors, as they’re kinda bitter it’s not “their” space to use anymore.

Not so much (in my opinion) a classic “attractive nuisance” since it hasn’t been an issue for other immediate neighbors who have a big playground, a pool, dogs, etc. none of them fenced.

Written By: tirojohns
Source: http://bit.ly/2KpnO0F