Volkswagen Tiguan Gearbox & Transmission Problems

Before they fitted the parts, particularly when they're expensive ones like the diff, they should have sought your approval to proceed. If they have, and you have agreed to fit the parts, you are liable to pay for them, even though they might not have fixed the problem. If they haven't got your permission to go ahead then you have grounds for refusing to pay for the parts. If they refuse to spend any more time on your car, or can't resolve the problem, you're really left with no alternative but to seek another repairer who would seek to solve it.