While Princess Camilla married a prince, gaining her mother's favour, Cristiana did not.
She say she later became aware of assets and money being transferred out of the trust fund by her mother, reportedly to prevent her from accessing her share.
In the latest development, a judge has threatened to fine Princess Camilla and her mother millions of dollars after she refused to reveal where certain assets that form part of the inheritance are, including a painting by Paul Gauguin.
"We have had not received any information about the Croci Group [the family business] or on Mdme [Edoarda] Crociani's non-voting shares in the group," Commissioner Julian Clyde-Smith said.
"The court believed [at the last hearing] that she knows where the Gauguin is. The way to purge the contempt is to tell us. And she has not done that."
Princess Camilla appeared at the Royal Court on the Channel Island of Jersey where she was issued with the order, just the latest in the lingering dispute.
It was 2010 when Cristiana first claimed she the trust fund was being unfairly accessed. The fund, called the Grand Trust by Edoarda, when became the subject of legal proceedings in 2011.
While Princess Camilla seemed to cooperate, informing the fund of assets, she was accused of leaving out items of value such as her mother's jewellery and a Gauguin painting valued at £49.9m.