I agree with all those who've said call the sheriff, animal control, or the troopers.  You have the dog on tape, on your property, in clear violation of the law.  There are fines in most communities, and they are often progressive - getting more costly each event.  It should not cost you to take them to court if they kill one of your animals.  That what the prosecutor is for.  That's his or her job.  If he or she won't do it, it's time to take those videos to the area TV station with your situation.  Just stick to the facts and it's amazing what will happen.
Each and every time you see the dog on your property, call the law.  Take photos, a pic is worth a thousand words and a video is even better.  It took several of our neighbors awhile to get the idea, but when the tickets starting getting up into the hundreds of dollars and they were going to be charged with a misdemeanor, they finally got the idea! 
When we had a pair of wandering dogs decimate our flock some years back, the law came out and took nice graphic photos for the judge.  We were reimbursed for the cost of the birds, the cost of the future lost eggs, everything.  Didn't cost us a dime.  
It's always best to not only be within the law ( yes, I know you can shoot a dog that is harrassing livestock), but to be as kind as possible.  If the neighbor complains about the fines, just mention you felt it was a better legal solution than shooting their pet. 
When we had a persistant problem with the son of a neighbor who would come to visit and let his dog loose (and he LOVED to chase chickens), and we caught him for the 4th or 5th time at our house (which was going to be a BIG fine) the father came down and asked if we could come to some kind of a compromise.  We agreed  that if they put in an invisible fence and showed the receipt and such to animal control we would not press charges this time.  When animal control showed up, he asked me" Do these people know how nice you are being to them?"  The point was, I would rather they spend the $$ on the fence, not on a fine.  That was over a year ago, and we haven't seen the dog since.
I know how frustrated you must be, but keep at it.  Good luck