Have you tried a Dog Box? It's basically a heavy-duty crate that your dog would need jaws of steel to escape. It's very expensive, but it's pretty much escape proof.
Try leaving her with a stuffed and frozen Kong or another long-lasting, yummy chew.
It has only been a month, she may not be comfortable with you yet, and if she can so easily go back to see the neighbor, she probably still thinks he is her owner. Why did the old owner give her up? Was it because of her separation anxiety? If he gave her up because of separation anxiety, you might want to consider medication. If she never had that problem with him, it's likely just that she doesn't understand he is no longer her owner.
Try leaving her with a stuffed and frozen Kong or another long-lasting, yummy chew.
It has only been a month, she may not be comfortable with you yet, and if she can so easily go back to see the neighbor, she probably still thinks he is her owner. Why did the old owner give her up? Was it because of her separation anxiety? If he gave her up because of separation anxiety, you might want to consider medication. If she never had that problem with him, it's likely just that she doesn't understand he is no longer her owner.