I can see a normal Eastern Rosella on the left, and a mutation Eastern on the right (a Rubino?). Tere is a black diagonal line on the right that looks suspiciously like the tail of a Princess Parrot.
There was no princess parrot in there. There were only three parrots. The one I didn't recognize is the one you decribe as an eastern rosella mutation, if it is the same as in this photo - [ame="http://www.flickr.com/photos/nvarvel/6156491781/in/set-72157627692369960"]Unknown Parrot | Flickr - Photo Sharing!@@AMEPARAM@@http://farm7.static.flickr.com/6208/6156491781_0db8501a43_m.jpg@@AMEPARAM@@6156491781@@AMEPARAM@@0db8501a43[/ame]