Well from the picture you provided, *very blurry at that) of the parents in the nest box, the father appears to show grey coloring on its neck and its rump between the wings, you might call it mauve as on the baby you say is mauve, but it appears grey in the photo's, also the father appears to have a definitive yellow pied spot on the back of his head, which explains the baby blue dominant pied progeny. For to get dom pieds in the nest one of the parents has to be dom pied. More clearer pics of parents might help. Cheers.