Well, I like that maple, too, though I only look at it once on your photo. But if it's really ruining your driveway, here's a compromise. Install a root barrier. Ask your town hall if you need a permit for that. Call 811 to mark out all the stuff underground. Start digging or rent a trencher. If the tree didn't survive, your neighbor can't object to cutting it down. If it does, everybody is happy!