It does seem strange that the vet would suggest waiting for the disaster before rehoming the dog. Particularly in light of the dog clearly being stressed enough to have hot spots.
On the other hand, I have been in the situation of having to make this decision. We decided to keep the dog (Ivy), because for us, we would not rehome her, knowing that she will bite without much warning. But we have put a TON of work into managing her every move, behavioral modification, and making sure Ethan is always safe. Ivy is the reason that I went from knowing how to train dogs, to learning how to modifiy problem behaviors in dogs. I had to learn a lot, very quickly, and luckily I had great access to mentors and teachers. This project (biting dog living with kids) is something I would not recommend to ANY client. It isn't something to be taken lightly, or without a committment to learning as much as humanly possible about dog behavior (and child behavior).
It is important to keep in mind the balance of the human's desire to keep the dog in the family vs. the dog's happiness with the situation. Sometimes what we want for the dog, is not at all what the dog would choose for himself.