A similar situation happened to my cousin, when they purchased their first dog, an English Springer Spanial. The difference being it was their neighbors that wanted the fence because the dog kept running into their yard. They didn't want the dog peeing on their grass. They had a hedge between the two yards, so after asking nicely if my cousing could please keep the dog on her own side, (she wasn't always watched outside) , They ran a chainlink fence on their side of the hedge.
So I'm wondering could you put something like that along your side of the trees? just an idea, I am always afraid of getting on the wrong side of people , lol , I'm a bit of a fraidy cat lol.