Nelson Mandela was "furious" that two of his daughters went behind his back to meddle in the management of his personal wealth, his lawyer has claimed in a case that exposes ugly battles over the lucrative Mandela brand.

Makaziwe and Zenani Mandela allegedly amended a trust deed in secret so they could gain access to the former president's wealth, according to court papers filed by Bally Chuene, the lawyer. The affidavit offers an insight into potential conflicts over the 94-year-old's inheritance. Some members of the family, whose wealth is tied into an opaque web of about 27 trusts, have been accused of exploiting the former president's global celebrity – a charge that Makaziwe rejects.

"Why are people obsessed with the Mandela family?" she demanded . "They are human beings like anyone else. They did not come from Mars. They have ambitions to be successful in life like anyone else, and I don't see anything wrong with that."

Married three times, Nelson Mandela has fathered six children, three of whom are still alive. He has 17 grandchildren. Blessed – or cursed – with Africa's most famous name, many of the Mandelas have gone into business; a few have dabbled in politics and two are starring in a much-derided reality TV show, Being Mandela.

Chuene's allegations are a response to Makaziwe, founder of the House of Mandela wine label, and Zenani, the South African ambassador to Argentina, who are seeking to oust him and George Bizos, Mandela's long-time friend and lawyer, from the boards of two investment funds. In an affidavit endorsed by Bizos, Chuene argues that the daughters' motive is to gain access to Mandela's money and sell artworks featuring his handprints. He contends that Makaziwe and Zenani have been trying to gain control of the Mandela Trust and became trustees without Mandela's knowledge since 2005.

Recalling Mandela's reaction when he found out, Chuene states: "Mr Mandela was shocked and used a common expression, 'Good Lord'. He was most infuriated and wanted to know when this had happened. He assured me that no such decision or approval had been given by him."

Mandela called a meeting at his Johannesburg home in April 2005. Makaziwe and Zenani as well as Bizos and Mandela's wife, Graca Machel, attended. "During this meeting, Mr Mandela made it clear to the applicants that he did not want them involved in his affairs," Chuene continues. "Mr Mandela wanted the applicants to resign their trusteeships."

Chuene accuses Mandela's estranged lawyer, Ismail Ayob, of colluding with Makaziwe and Zenani. Mandela "had become concerned that artworks were being sold, ostensibly on his behalf, without his authority or permission", Chuene said.

In June 2006, another meeting was held at Mandela's home. Chuene claims: "The meeting was very heated and, in some respects, unpleasant. Mr Mandela was furious that the applicants had allowed themselves to be used by Mr Ayob and had continued to associate themselves with him, knowing full well that he had terminated his relationship with Mr Ayob.

"He was, moreover, upset that they continued to be involved in his personal affairs despite his clear instructions to them at the previous meeting held in April 2005."

According to Chuene's affidavit, filed at a regional high court in Johannesburg, the wounds reopened in August 2011 when Zenani asked for trust money to be distributed to them and other beneficiaries. Bizos was reluctant to do so, citing legal and tax implications.

He says Bizos's reservations were confirmed after a bank requested the original trust deed for the Mandela Trust. It had been covertly amended by Makaziwe and Zenani in 2005, he alleges.

He goes on to claim: "It was evident from the purported amendment of the trust deed that the applicants had clandestinely and with the assistance of Mr Ayob sought to secure control of the Mandela Trust, contrary not only to the wishes of Mr Mandela, but also to the terms of the trust deed."

On Friday, Makaziwe declined to address the claims directly, while Zenani was unavailable for comment, but Ayob said: "The Mandelas will respond to the allegations within the timeframe allowed."

With the former president frail and his lucidity dwindling, some fear the case is indicative of a looming, unseemly struggle for his legacy. "The squabbles will be bitter and vicious if the first salvoes in this war are anything to go by," warned the Star of South Africa. Mandela's personal wealth is a mystery, but one veteran journalist who has followed him closely put it at 150m rand (£10.5m).

In the court papers, Bizos, 84, raises concerns about how it might be carved up. "As a confidant and adviser of Mr Mandela, I know that his wishes in relation to the three general trusts established by him was that these ought to provide long term assurance, to the extent possible, for the support and education of the beneficiaries, which would include generations to come," he states.

"I was, accordingly, concerned to learn in the last quarter of 2011 of a proposal for the distribution of almost the entire capital of the Mandela Trust in lump sums to groups within the broader Mandela family."

About 27 trusts containing a roughly estimated 50-60m rand were created by Ayob in the 1990s. He admitted that this was "tax advantageous" because it split the income between different individuals, but he denied that was the sole reason.

"It's fairly routine with large families with a lot of money to create trusts for the beneficiaries," he said. "It's very simple: you have one child who says as soon as I get my inheritance, I'm going to get a Jaguar, and you need a balance in terms of who gets the money. Everyone has different needs. It's very difficult if you only have one trust."

The Mandela name can inevitably open doors. The family is active in more than 110 trading companies, according to records compiled by Beeld newspaper. Makaziwe is reportedly an active director in 16, including Nestlé South Africa, although she insists some directorships have lapsed.

An emotional Makaziwe responded to critics who accuse the family of exploitation. "It's our name anyway," she said. "Why should we apologise for our name? I'm in the wine industry. There are families who've been in the wine industry for 500 years and no one says they are cashing in on their name. Every child in this family who wants to use the Mandela name has a right to do, so as long as they do so with honour and integrity and upholding the values of my father."

Noting that many other commercial operators use Mandela's name and image, Makaziwe added: "It's the height of madness. I know what I am. The fact that someone calls me greedy is not going to make me greedy. Are they saying because I'm Nelson Mandela's daughter I'm not allowed to be a company director?"

Not all the Mandelas have been successful. Grandson Zondwa Gaddafi Mandela was a director of Aurora Empowerment Systems, a mining company that went into liquidation and was named by unions as the country's worst employer. Last year Zondwa established a company called Mandela 95TH Birthday (Mandela turns 95 in July). Asked for details of the venture, Zondwa requested that questions be submitted by email, but he had not replied by Friday afternoon. He said the inclusion of Gaddafi in his name was a long story.