Neighbors' dog treats our property as its own; what are our rights?

Your county should have a law on this, or your city! Try to talk to them and tell them your Mom fears dogs. If you can't talk to them wright a letter to them! If they refuse to do anything, call the law or dog catcher. Most lab's aren't mean, they might bark at you but few will attack you. Just raise your arms and yell at him, he should run off. Or you could try putting some RED pepper on the ground, or spry bleach around, I know it keeps racoon's and just about anything else away