I'm assuming that's the price for a board and train. Even so, that sounds ridiculous. And you said it yourself - your sister is not taking care of the dog. Even if you do send it to that trainer, the trainer will teach it and occupy it for 3.5 weeks, then it will come back home and devolve into boredom behaviors again because it is still not being cared for.
I say give your sister a swift kick in the butt so she learns to take care of her dog. She needs to actually take it to some classes and learn to train it herself, and learn to meet her dog's mental and physical stimulation needs. Or she needs to rehome it to someone that would actually appreciate it.