How Toadsworth got the Bros. to Brooklyn theory: He used a very mystical warp pipe kept secret and protected by the royal family that was only to be used by the royal family in case of a really really really really really bad emergency. Any use of the warp pipe if the emergency was not dire, was strictly forbidded because no good ruler should runaway from the problem the Kingdom is facing. Since it was so ancient nobody knew where it went exactly, but Toadsworth knew that to protect the kingdom and the Bros. from future attacks that he had to send them away so he did. Even though the Mushroom Kindgdom lost a war and the Kingdom fell into the hands of the Koopa Empire, he was still able to protect the Bros.