Mucca is incensed that Macca wants Bea's step-sister Stella on a board of trustees being set up to look after the four-year-old's financial future.
Heather, 40, has vowed to challenge the move-taking the matter to court if neccessary.
She has long been an sworn enemy of 35-year-old fashion designer Stella and blasted: "Keep that woman away from my daughter and my life."
Sir Paul is adamant he wants Stella to play a key role in Bea's future-in case anything happens to him before her 18th birthday.
But a source revealed: "Heather wants none of it, and has told Paul in no uncertain terms that she will fight any role Stella has in Bea's life."
She and Sir Paul are currently sweating on the result of their court divorce settlement-and how much of Macca's £825million Heather will actually get for the four-year marriage.
Meanwhile Mucca was also angered by Macca pulling the plug on a divorce deal over her security-claiming it could lead to her being attacked.
Sources say she screamed at him in a furious row last week: "I'll be dead in three months."