Is it possible to move a planet out of its orbit? At least a lighter planet?
Yes. Even with todays technology we can get started.
In this article by Korycansky et al 2001 it is suggested to use rockets to move an asteroid (like a larger version of the NASA ARM Asteroid Redirect Mission) to a cycling orbit between Earth and Jupiter. The asteroid would pass near infront of the Earth in order to give the Earth a slight gravity assist which moves it outwards. The asteroid then passes near behind Jupiter to itself get a gravity assist. This transfers energy from Jupiter's to Earth's orbit. I've also heard of a proposal to use Venus instead.