For a dog that's raised outside and has never lived inside, she doesn't know what she's missing.
But if you take that same dog and bring it in the house for over a year, where she gets to be around her family the majority of the day and night, gets to sleep in a climate-controlled room, and doesn't have to worry about keeping strangers and other animals off her property; and then make that dog live outside again, then yeah, it would definately be a shock and lead to stress and frustration.
Stress and frustration lead to barking; your dog is barking because she's stressed and frustrated about living outside. Putting a bark collar on her will only raise her stress and frustration levels. While it may stop her from barking, it will also lead to other stress related behaviors, such as digging, climbing out of the yard, aggression at the fence, etc. There are a lot of dogs and situations where bark collars are a good choice, but I strongly argue that this is NOT one of those situations.
Maybe instead of having the dog live outside with you, you could work with your parents to figure out how to make their lives easier with the dog. Maybe this means taking the dog to training classes, taking her out for a run a few times a week, helping them work on crate training or other housemanners the dog might be lacking in, etc.