Megan Preston and co-accused Steven McGregor used an imitation firearm to rob passers-by in the park after downing a cocktail of alcohol and valium.
Her mother, Christine, said her daughter was expecting a jail sentence of up to six years when she is sentenced next month.
But the 47-year-old said her daughter was suffering from a bipolar disorder at the time she went on the crime spree and had run out of medication to treat the condition.
Mrs Preston, who works as a nurse, said she was planning to submit a formal complaint to NHS bosses over their handling of her 24-year-old daughter’s treatment.
The mother-of-two said her daughter “fully admits her guilt” in carrying out the terrifying hold-ups, and was mortified that she had left the victims “afraid they were going to die”.
Preston and McGregor, 25, pleaded guilty at the High Court in Edinburgh on Thursday to targeting 12 people between midnight and 1am on March 29, threatening them into handing over cash and valuables using a dummy firearm.
The rampage was only ended when one of their victims fought back and disarmed them.
Mrs Preston, who lives in Gilmerton, said: “Megan is not saying she did nothing wrong. She is an intelligent educated girl and fully admits her guilt for what happened.
“Her lawyer has told her to expect a sentence of between four and six years. We’re hopeful that when her medical history and the circumstances are given in mitigation then she won’t get as much as that, but we’re preparing for the worst.
“Megan has talked to me in prison about how absolutely devastated she is about what happened. She’s distraught over what the victims went through. She is fully remorseful and can’t believe she did that to people.”
Mrs Preston said her daughter, who had studied to become a vet, has a history of self-harm, which included at least two suicide attempts, and had suffered from bipolar disorder since her mid-teens.
She added: “On the day this happened, Megan admitted to me that she had run out of medication.
“I went to a health centre to a get an emergency prescription but I was told Megan would need to see a doctor first. The earliest available appointment was April 12.
“If Megan had received the proper level of care then maybe this would not have happened.”
Professor Alex McMahon, director of strategic planning and primary care, NHS Lothian, said: “We would urge anyone who is unhappy with any aspect of their care to write either to their individual GP or to our complaints department so that the matter can be looked into.”