Sounds wise after the event but were this me and given this was bought from Stoneacre I'd have insisted the deal was only going through if they supplied the car with two fully functioning VAG keys. There's too many dodgy cars out there - sis in law bought a VW Gold diesel via Network Q a few years back and despite all the checks they did it turned out o be a ringer. They gave her a refund but in my view a reputable dealer wanting to remain the same doesn't sell a car with only one dodgy key.
Soz - not a solution, not witty just an observation. If I were you I'd see if they'd take it back coz I bet at [present nobody would buy it off her.