Landed and waited for the other planet to wash over the ship. It was moving at a freaky fast speed! Also no you can't simply drive an SRV from one planet to the other, tried it.
I didn't try to drive my SRV from one planet to the other...but managed it anyway. The game crashed on me during the event, and when I logged back in my SRV had switched bodies. Meanwhile, my ship was still orbiting the body I had landed on, so I couldn't recall it.