The 39-year-old was attacked in the carpark outside the hospital in Kilmarnock at around 7:45pm on Thursday, February 4.
Just minutes later, her daughter, Nichole Anderson, 24, was attacked in Portland Street in the town.
She was died in hospital from her injuries.
Shortly afterwards, Steven Robertson, 40, died in a crash on the C50, between the B7036 and A76.
Police Scotland has confirmed that all three deaths are linked.
In a statement issued on Monday afternoon, John Burns, Chief Executive of NHS Ayrshire, where Ms Robertson Coupland worked, paid tribute to the nurse.
He said: “Following the incident at University Hospital Crosshouse on Thursday 4 February 2021, we can confirm the sad death of our colleague, Emma Robertson.
“Emma was a valued member of our Domestic Services team, and she will be sadly missed by her colleagues.
“Our thoughts and condolences are with Emma’s family, friends and colleagues. We would ask that the media respect the privacy of those involved.”
He added: “We have increased the staff care support available to our staff, and we are encouraging any members of our staff who have been affected to take advantage of the support available – whether that is by calling our helplines and speaking to a member of the staff care team, or attending the staff wellbeing hub.”
A GoFundMe page set up in the wake of the mother and daughter’s deaths has now amassed more than £22,000.
The organiser wrote that everyone was “absolutely devastated and heartbroken” by the news of the pair’s death, adding that the funds raised will be used “to help try and ease the financial stress of worrying about paying for their funerals.
"Even if it’s just a pound each, every little helps.”
You can visit the fundraising site here.
Formally identifying Ms Robertson Coupland and Ms Anderson on Monday, Police Scotland appealed to the public for information relating to their deaths, as their investigation continues.
Chief Superintendent Faroque Hussain, Local Policing Commander for Ayrshire Division, said: "As you can imagine, the families of those involved are absolutely devastated and still coming to terms with what has happened. They have requested that they be allowed to grieve privately at this time.
"The investigation into the circumstances surrounding their deaths, which are linked, are ongoing. We are not looking for anyone else as part of the inquiry.
"The local community has been very supportive of our enquiries so far but we are still appealing for information, especially dashcam or mobile phone footage from the car park at University Hospital Crosshouse between 7.30pm and 8pm on the Thursday night.
"We’re also eager for anyone who may have been in the Portland Street area between 7.45pm and 8.15pm, and anyone travelling on the A76 between the Bellfield Interchange and Ochiltree between 7.50pm and 8.45pm, to get in touch.”
Anyone with information can contact police on 101, or submit this directly to officers via the Major Incident Police Portal here.