Could someone local with the same brand locking wheel nut not help or are every single key they make different?
Like said try tighten all 4 bolts around the nut and try that way!
Was it done at Kwik-Fit? If so my brother works there and all normal nuts can be buzzed gunned on but they are NOT aloud to use the air gun on locking wheel nuts, it's company policy, if that's the case then get back to them and explain as it was tightened with the gun it has caused it to snap, they then need to get it removed!
Hope this helps!