The row centred on plans to promote two paths close to the Queen's retreat in Royal Deeside to walkers and tourists.
A letter written by Ms Cunningham on 10 December revealed she was "minded" to include the routes in the Cairngorms National Park "core paths plan", despite advice to the contrary from the Home Office.
Home Office officials had informed the Scottish Government that bringing in more walkers and cyclists would increase security risks.
Nevertheless, her letter showed that she wanted to press ahead with plans to publicise the paths anyway. "I am not persuaded that this (increased security risk] amounts to sufficient reason for excluding these two paths from the core paths plan," her letter to UK security minister David Hanson said.
Ms Cunningham, whose nickname is Republican Rose, was only dissuaded from her plan when Mr Hanson wrote warning her he would contact the Home Secretary and Scottish Secretary and take action at Westminster to overrule her decision.
Mr Hanson said including the paths at Ballochbuie and Glen Muick in the scheme presented a "security risk to the Queen and her immediate family".
Ms Cunningham's behaviour led Adam Ingram, the Scottish Labour MP and former Northern Ireland security minister, to call for her resignation.
He accused Ms Cunningham of letting her "personal prejudice" overtake advice, and said: "She is simply not fit to hold office.
"Ministers always have the right to reject advice but never when it puts the lives of others at risk.
"Alex Salmond must take control of the situation and require her to resign."
At First Minister's Questions, Mr Salmond defended his minister, describing Labour's criticism as "absurd". He said: "Everything in this government, according to this issue, has been carried out by due process."
He said Ms Cunningham had written to Mr Hanson before she made her final decision on the matter. Mr Salmond said she was "writing to establish whether there is any additional information about security considerations".
Mr Salmond added that her final decision to exclude the paths was made on 11 January, the day she received Mr Hanson's reply.
However, Labour maintained the only reason Ms Cunningham had backtracked was because Mr Hanson had threatened to overrule her.
Mr Salmond also called on the Home Office to investigate who had leaked the correspondence between the two governments. He argued that highlighting it had served to publicise the two paths, an outcome that went against the police's desire to draw as little attention to them as possible.
Eddie Barnes: Is there OS map of Tora Bora somewhere?