It just depend how hard you push to be honest. For a car to have a major fault within 2 weeks of collection, and for them to say wait till April 7th, is out of order, and they're just booking it in as if for general work or a service.
Speak to salesman, and insist car taken back that day. Speak to manager and say the same. They'd have found you a car no problem, even if it's a demo car. Accept the first answer from the customer service desk, and you'll get nowhere.
Everyone's different, but I'd have stood in the dealership, and not left till I got a car. The last thing the manager wants or needs is for a disgruntled customer making a fuss in front of other potential customers. The car should be tip top if sold via an Audi dealership. Anything less, then they need to deal with it straight away. New or used, it doesn't matter.
Edit to add.
Again if it was me, I probably wouldn't accept a repair either. My confidence in the car and the dealer would be ruined. Money back, and buy elsewhere