That is what I was wondering. You would most certainly qualify for a World's First then in Palm Cockatoo breeding.

Nobody (breeders in Europe, UK, USA and elsewhere) has ever had 2 eggs laid as part of a single clutch. Especially if there is only one hen with a single male. From your description, chicks hatched from both eggs which must obviously mean that both were fertile and the egg interval is not too long in between as you are able to compare both chicks.

Does your male incubate as well or just the female?