We have torn down nests before. They just go and build across the street. They seem to know where our boundaries are. That is not far enough away. The babies are so loud that I can hear them in the house when they are across the street. The adults seem to recognize that DH and I are enemies. The second anyone opens the door, they fly to the property line.
This is probably an unsolvable problem. We need them to stay 200 yards away and we can't control what goes on in the neighbors' yards. Baby mockingbirds are extremely loud. I may have mentioned this before, but the only common things louder are the trash truck and a leaf blower.