"I'm in the process of buying some of my neighbors yard "
I'd figure out where else you can move this heap while they are working on your project. your yard somewhere, perhaps? Offer to help push it. Trade an old scooter for it and sell the car for scrap? I would try to NOT make any ultimatums or tell half truths. or get between family. You have to live next door to your neighbor, so use the carrot, not the stick!