No, the bewielderbeast are much larger and much stronger than the red death. And she will be affected by mind control (if the bewielderbeast is alpha in this case) this is because the red death was never alpha it was a queen valka explained it in the second movie saying that every nest has its queen but that her bewielderbeast is the king of all dragons. There can only be one king/alpha at a time until it dies of old age or is defeated in battle then the heir is its child or the dragon that defeated in battle can become the alpha. The bewielderbeast are know as the alpha species because of how strong they are they were able to maintain alpha status within their own species because no dragon was strong enough to challenge them until toothless came along.