I didn't read the responses so some of this may be a repeat...
First I have ZERO tolerance for a ill mannered dog! Regardless of breed. Your cousin should be glad she is not my neighbor because if I caught her dog chasing my livestock, the dog would be dead. The three "S's"- shoot, shovel, shut up.
Border Collies(actually any cowdog) are very smart, they have to expend that energy. Any dog that is bred to work will become obsessive and neurotic if not trained properly and has an outlet for using the training and ridding itself of excess energy. It is your cousins fault, not the dogs for not providing the leadership and exercise. The dog is forced to find it's own work rather your cousin providing the work for her.
Yelling at a dog does no good when you are constantly yelling at it. It is the same tone so it means nothing. I use my voice sparingly with my dogs and if I do raise my voice they know they are in trouble. Also once the dog gets a hold of a chicken and kills one it is nearly impossible to break them of killing chickens. It won't be to much longer and your grandmother won't have any chickens.
I am not sure whether you stated who's property this happening on but frankly I wouldn't care if the dog was biting my horses. I would tell your cousin to get the dog out and tie it up or you will beat her with the lunge whip. Obviously she has no desire to do any training so maybe you need to train your cousin.lol
That ain't much of a solution, but if your cousin isn't willing to do anything with dog, their isn't a whole you can do unless you are willing to a little training yourself.
These situations infuriate me! It is like parents who have brats for children and blame it on something else. No accountability.
I DON'T LEAD 'EM AND FEED 'EM, I RIDE 'EM AND SLIDE 'EM.