Can We Move PLANET EARTH Across the Universe?

Interstellar travel is horrible-what with the cramped quarters of your spaceship and only the thin hull separating you from deathly cold and deadly cosmic rays. Much safer to stay on here Earth with our gloriously habitable biosphere, protective magnetic field, and endless energy from the Sun. But what if we could have the best of all worlds? No pun intended. What if we could turn our entire solar system into a spaceship and drive the Sun itself around the galaxy? Well, I don't know if we definitely can, but we might not not be able to.