I didnt read all of the responses, but I just want to say, You can't train out what is bred in. You can only control it and direct it in a diffrent direction.
I have very drivey JRTs. You can't imagen how meny toys we go through between the two of them, and on is only 12 weeks old. I don't hunt, but I do take them to lure coursing, and we do other JRT stuff at the house. I have more wholes in my ard than I could count. That's just the way they are, if I didnt want holes in my yard, and stuffing all over the house then I wouldn't have gotten a Jack Russell.
Sounds to me like your cousin needs to rethink her resons for keeping this dog. I can't figure out why she would want that dog in the first place? She obviously didnt do any research.