Being the king's slave is spoken of as being an animal on to the shoulders of which the king puts a yoke so it can do heavy work. AT: "and whose people do not willingly become slaves of the king" (See: [[rc://en/ta/man/translate/figs-metaphor]])
The hand here could be a metonym for Nebuchadnezzar's power, or it could be a metonym for Nebuchadnezzar's armies. AT: "I have used Nebuchadnezzar's power to destroy it" or "I have enabled Nebuchadnezzar's armies to destroy i" (See: [[rc://en/ta/man/translate/figs-metonymy]])