Elizabeth Smyth claims Deirdre Romanes did not know what she was doing when she gave instructions about what was to happen to her £4.6 million estate. She has accused her late sister's ex-husband, Monaco-based Iain Romanes, of persuading her to change the will.
A will drawn up some two years earlier favoured younger sister Ms Smyth, of County Meath, Ireland, and she has already won a court decision blocking the sale of prestige property in Edinburgh's New Town until the issue is resolved.
Mrs Smyth wants judge Lord Glennie to set aside the later will as Mrs Romanes, of Edinburgh "lacked capacity". The court papers claim Mrs Romanes was weak and facile and easily imposed upon, allowing Mr Romanes and three other individuals, named as her executors, to get their way.
If the second will stands, the bulk of Mrs Romanes' estate will be ploughed, through a trust fund, into the Dunfermline Press.
Mr Romanes, who left his wife for another woman, continued to be a director of the company after the marriage broke up in 2001 and holds a block of shares.
Sixty-year-old Mrs Romanes died in May 2010 after a long battle with cancer which she had kept secret, even from family and close friends, until the end.
For two years before her death the newspaper had been in trouble and managing director Mrs Romanes was said to be determined it should keep going.
The second will, which instructed a payment of £3m into Mrs Romanes' Liferent Trust, was seen as a way of doing this.
The hearing is expected to last two weeks.