So far she has been rebuffed. She has threatened to sell the shares if she doesn’t get her way.
What makes this more than a share dispute, however, are widespread fears in Australia that Rinehart is trying to exert more editorial control over the papers. She has, for example, been critical of the media’s reporting on climate change.
Meanwhile, the climate within Rinehart’s own family has gotten chillier. She has been battling her children over the family trust for months. According to an article in the Sydney Morning Herald, her son, John Hancock, has enlisted the financial help of a mystery Chinese benefactor to help him remove his mother as a trustee.
''I've got quite a few friends in Asia and one of them offered to help me via a fundraising party in Hong Kong, so he managed to get about 30 people who all gave me a substantial sum of money,'' Hanckock told Australian television. ''He also introduced me later that night to an extremely wealthy Chinese man who is helping me.'
It all sounds like one of those Nigerian emails: “I have a fortune that I need your financial help to retrieve.” Only this time, it may be real.
Rinehart may have the best intentions when it comes to both newspapers and her family. But the ongoing dramas and power struggles have made one of the world’s richest women also among the most controversial.
-By CNBC's Robert Frank
Follow Robert Frank on Twitter: @robtfrank