Moon position

Why Moon is not a planet? It is because of its seize but more because of the content of biochemical matter. Why our Moon is not a moon of another planet? Somehow core reacted and reacts to core of the Earth in magnetic way of matter. If will something happened to the Earth in the future, we might lose the Moon? Maybe yes. But what would happen with Moon then? What would lead it to change position? Will it stay within Solar system? This is not a simple answer.
All big objects in our solar system and the universe have gravitational forces among them. It means that even if Earth disappeared, the moon would still be influenced by other objects. Moon will change position and become part of other planet's space.