Not sure where he actually was when Mountbatten died, but what if on 27 August, 1979 Charles drops in to see Mountbatten and is killed when the bomb goes off?
Anti-Irish attacks skyrocket on the mainland. The British public, who were IOTL really pissed off about Mountbatten, are not going to take kindly to the murder of the heir to the throne at the same time. I would imagine a strong, concentrated anti-Irish feeling resembling the immediate hysteria in September 2001 against Muslims from some sections of the US population.
Would Andrew be King Andrew I? Doesn't sound very good. His middle names are Albert, Christian and Edward. Edward IX, perhaps?