Clare Lally condemned Campbell Gunn after the First Minister’s special adviser complained in an e-mail about her description of herself at a Better Together rally.
She told crowds she was just a “normal person” whereas Mr Gunn said she was closely aligned to the Labour party.
He also said she is the daughter-in-law of a former Labour Glasgow Lord Provost, which she is not.
Mr Salmond faced calls to sack his adviser as opposition leaders accused the aide of using “bully-boy tactics” against the mother-of-two from Clydebank.
Last night Mr Gunn was still in his post – which carries a salary of between £39,445 and £83,963 – after being told to apologise by Mr Salmond.
Mr Gunn, a former political journalist, apologised “unreservedly” for the offence and upset he had caused to Ms Lally and her family.
Ms Lally, 33, however, said she would not accept Mr Gunn’s apology, saying: “I don’t think it’s an apology, it’s a bit of an insult. I think I am only receiving the apology from him because he has been caught out. The e-mail and inaccurate information has been shown for what it is. It is an attack on myself as a mum, as a person and as a parent. I won’t be accepting this apology.”
The damaging row was triggered when Mr Gunn took exception to comments made by Ms Lally when she appeared at a Better Together rally in Glasgow on Monday.
Arguing for Scotland to remain within the UK, Ms Lally described herself as a “normal person” who wanted to do “something extraordinary” by doing her bit to keep people together.
She said she was grateful for the care health workers had given her seven-year-old twin girls, one of whom has cerebral palsy, and wanted to “make sure our NHS remains the best in the world”.
Her remarks were quoted in a newspaper, which then received an e-mail from Mr Gunn saying: “You are no doubt aware that the ‘mother-of-two’ who described herself as ‘just a normal person’ in the Telegraph today is actually a member of Labour’s shadow cabinet and daughter-in-law of former Labour Lord Provost Pat Lally…”
In fact, Ms Lally is no relation to the former Glasgow Lord Provost.
She has, however, been appointed to Labour’s shadow cabinet as a “carers’ champion”.
Ms Lally pointed out that the First Minister has visited her home in the past to discover more about her work looking after her seven-year-old daughter, Katie, who requires 24-hour care.
The points made in Mr Gunn’s e-mail were echoed on the Nationalist supporting website Wings over Scotland, which claimed that Better Together was “misleading people by presenting hardcore political activists as normal every day folk…”
Ms Lally’s contribution to the independence debate was also discussed in far more abusive terms on other social media outlets – including one which described her as: “A liar now and forever whatever the outcome of the vote, a known Quisling and collaborator.”
The online abuse became so poisonous that Ms Lally closed down her Facebook and Twitter accounts.
Describing the unpleasantness of the internet abuse, Ms Lally said: “For the last 48 hours it has been absolute hell and that is because of him [Mr Gunn].
“An apology is not going to stop or take away the things that have been said about me and my family. It is more of an insult than an apology.”
Opposition leaders claimed that the online abuse had been “unleashed” by Mr Gunn’s attack and called for him to be sacked for breaching the special advisers’ code of conduct.
This specifically prohibits “the preparation or dissemination of inappropriate material [and] personal attacks”.
It adds: “Any special adviser ever found to be disseminating inappropriate material will automatically be dismissed by their appointing minister.”
Mr Salmond said: “The mistake was that one of the special advisers thought she was Pat Lally’s daughter-in-law.
“She’s not Pat Lally’s daughter-in-law and I have told the person concerned to apologise for that.
“I don’t regard that as an insult, incidentally, being Pat Lally’s daughter-in-law. I have told the special adviser to apologise for any offence caused.”
Mr Gunn, a former political editor of the Sunday Post, said he was “genuinely sorry” and that Mr Salmond had “no knowledge” of his e-mail, adding: “Nothing in the e-mail I sent was intended in any way to be a personal slight on Ms Lally or question her absolute right to express her views, and I apologise unreservedly for the upset and offence that has been caused to her and her family.”
Mr Gunn added: “I deplore online abuse directed against Ms Lally or anyone else – from whichever side in the referendum debate – and the assertion by the No campaign that I had any involvement in the coordination of such activity is completely untrue. I sent one e-mail to one journalist which in no way was intended to form the basis of a story.
“I am genuinely sorry I did so, and the First Minister had no knowledge of it. The First Minister has previously met Ms Lally, as is also reported today, and holds her in the highest possible regard.”
But Labour leader Johann Lamont accused the adviser of having “launched the most disgusting personal attack on a mother who cares for her disabled child because he doesn’t like her views on the referendum”.
She added: “Apologies are not enough. Alex Salmond must sack his senior adviser Campbell Gunn. Campbell Gunn’s attack on Clare Lally unleashed a tidal wave of vile abuse aimed squarely at her on the internet which caused Clare and her family immense distress.
“Once Campbell Gunn is sacked we can then ask the many further questions this disgusting incident throws up. Did Alex
Salmond sanction this attack? How far reaching is the First Minister’s grip on the Nationalist machine which abuses and traduces his opponents?
“But the regulations are quite clear. Special advisers cannot indulge in vile, personal attacks like this. For once Alex Salmond should enforce the rules and sack Campbell Gunn.”
Conservative leader Ruth Davidson said: “For such slurs and misinformation to be spread by one of the First Minister’s taxpayer-funded key advisers is a new low for the SNP government in this referendum debate.
“This was nothing but bully-boy tactics towards someone who had the temerity to disagree with the SNP.”
She added: “We need urgent clarity on whether this government aide was carrying out the orders of Alex Salmond or any other government minister.
“This cowardly attack on someone’s character cannot simply be brushed aside by a forced apology.”