Scholastic Corporation, set up by Robinson’s father a century ago as a magazine for teachers and pupils, publishes some of the world’s most popular children’s titles, including Captain Underpants, The Hunger Games, Clifford and The Magic School Bus.

Now, new court filings reveal that Mr Robinson’s two sons are exploring avenues to challenge her right to the controlling stake of the company and that Ben declined to sign a document waiving his right to contest his father’s will.

He later received a court summons from Ms Lucchese’s team in October seeking a response, according to legal filings.

The family also believes Mr Robinson was at work on a new will when he died, they said.

While rumours of the relationship between Mr Robinson and Ms Lucchese have been described as an “open secret” by employees speaking on condition of anonymity, it appears that the sons were never told directly, even when a pair of Prada boots were found at home.

It has been claimed that Mr Robinson lavished Ms Lucchese with gifts over the years, including a Porsche Cayenne, a New York City apartment and a $500,000 pink diamond ring.

His ex-wife, who worked at Scholastic for more than three decades and divorced Mr Robisnon in 2003, is supporting her sons’ legal efforts. In an interview with the Wall Street Journal, Ms Benham said that Ms Lucchese’s control of Scholastic is still in question. “She’s sitting on top of a mountain of gold, but the question is whether she’s got the gold,” she said.

There were hopes that the situation could be solved without a fight.

In the summer, Reece said that while the contents of his father’s will were “unexpected and shocking,” what he wanted most was “an amicable outcome.”

Ben, who operates a sawmill and workshop in Martha’s vineyard added: “We’re expecting to have a collaborative approach with the estate.”

Ms Lucchese, who is Canadian, joined the company in 1991 and in 2014 became chief strategy officer. If granted the controlling stake she could decide the leadership and direction of the company.

Scholastic spokesman Anne Sparkman said of Ms Lucchese: “Iole is committed to doing what’s best for all stakeholders, including the Robinson family. She’s trying to work constructively with Mr Robinson’s sons.”