We moved to a farm that was canopy to canopy with red oaks. Our approach was to tell our 7 and 9 year old about the rules and possible death. It worked for us.
We use the **** out of liability waivers for anyone that comes to our place. There are trees, snakes, livestock, water and I don't want some ******* trying to sue me if their kids gets crushed by a horse or cattle. You may look into that as well from the sounds of your neighbors.
Everyone can **** off. It's your house and your kids. You decide your level of risk tolerance. You make the decision for you.
Honestly, you should get on nextdoor and put your OP there for the LOLZ.