Kimberly Darroch, whose ten-year-old daughter Milly Main died at the Queen Elizabeth University Hospital (QEUH) campus in 2017 after contracting an infection, and Louise Slorance, whose husband Andrew died last year, both called for the health board’s leadership to be removed.
Ms Darroch said she was "absolutely disgusted" by photographs showing mould growing at the hospital, and called for the facility to be shut or wards moved.
Ms Slorance said: "The insides of the hospital need ripped out and let's make sure there's no mould in that building or any other."
Her husband Andrew, 49, was a senior Scottish Government official. He was receiving cancer treatment at the QEUH when Ms Slorance believes he contracted Covid and another infection she was not told about.
The two women were speaking at a press conference in Edinburgh organised by Scottish Labour leader Anas Sarwar, who insisted Ms Sturgeon and the Scottish Government now needed to "pick a side".
His party tabled a motion in Holyrood declaring no confidence in the health board leadership, but this was rejected by SNP and Green MSPs.
Mr Sarwar said: "Today represents an opportunity for us to draw a line in the sand and to say enough is enough.
"Since this tragedy took place, since this hospital has opened and since the litany of failures, no one – not a single person – has been held to account."
He added: "What we are saying directly to the First Minister, directly to the Scottish Government, is they have a choice and they now have to pick a side.
"They are either going to pick the side of Kimberly Darroch, Louise Slorance, all the families and of the senior clinicians, and say enough is enough.
"Or they are going to take the side of senior managers who have allowed these failures to happen."
Mr Sarwar said the past two years had seen ignored reports, staff bullying claims, infected patients and deaths, ward closures, the launch of a public inquiry and a separate criminal investigation, adding: "Despite all of that, not a single person in this organisation has been held to account. Why?"
He said: "If this had happened anywhere else in the UK, if this had happened anywhere else in the world, there would be resignations and there would be sackings.
"But in Scotland we're expected to turn a blind eye, we're expected not to ask difficult questions, and rather than the pressure being put on those who are making those fatal decisions, instead in Scotland we have a culture where we attack those asking the difficult questions."
Mr Sarwar was speaking after a group of senior clinicians at the QEUH complained of “unfounded criticism” of clinical teams and staff.
In a letter to the First Minister and health secretary Humza Yousaf, 23 senior figures expressed their "immense frustration”.
They wrote: “As NHS Greater Glasgow and Clyde clinicians and clinical leaders, we write to express our immense disappointment and frustration about the way in which our hospitals, our colleagues and the treatment of our patients is being portrayed in the press and the chamber of the Scottish Parliament.”
The clinicians said the “unfounded criticism of our clinical teams and staff as well as the safety of our hospitals” was “hugely detrimental to staff morale at a time when so much is being asked of them”.
But speaking at the press conference, Mr Sarwar insisted: "Let me say this directly to the Scottish Government, to the health board, and to anybody else that's listening. I will not stop, I will not rest.
"I will remain on the side of these families until justice is delivered, we get the answers and those that are responsible for this are held to account."
Mr Sarwar said he had "full confidence" in frontline NHS staff, but "no confidence" in the leadership of the health board.
He added: "I warn them – do not gaslight the entire staff base of a hospital in order to protect your job.
"Instead do the right thing so we can protect patients and their families stop infections, so no other family has to go through what both Kimberly and Louise have had to go through over the last four years in the case of Milly Main, and over the last year in the case of Andrew Slorance."
Ms Slorance said: "We need to know that Andrew's and Milly's death is not in vain. Action needs to be taken now.
"If we wait for reviews, or the completion of the inquiry, how many more families will suffer this loss in the meantime?"
She added: "The erosion in trust is about the management."
Ms Darroch said she had been fighting for answers and transparency for the last two years "in vain".
She said nothing had been done, adding: "There's continued secrecy. There's continued bullying.
"And we're here today to say enough is enough. We need the health board to be held accountable.
"We need them to be removed from the job they're doing in order for patients, families and the general population of Scotland to have trust in that health board."
She said she had no issue with clinicians and frontline staff, insisting her daughter’s treatment was "second to none".
Ms Darroch said the "breakdown in trust" was down to the hospital building itself and the leadership.
Asked how it made her feel to hear Ms Slorance's story, Ms Darroch said: "It has made me feel really angry.
"We have worked tirelessly to stop this from happening again, and that was my main focus after Milly died, and the reason that I basically came into public life was so that no family had to go through what I went through.
"That hasn't happened. It has continued to happen and it will continue to happen until something is done about the leadership of the health board."
Ms Slorance added: "I think the Scottish Government now need to show whose side they are on, whether it's ours or the health board management team."
Speaking in Holyrood, Mr Yousaf said he took exception "to this line about whose side are you on".
The health secretary said: "Each and every single one of us wants the best, most safe patient experience for members of the public. We are all on the same side."
He highlighted the letter from the 23 senior clinicians, and urged MSPs not to dismiss their concerns.
Mr Yousaf’s amendment to the Labour motion also pointed to the ongoing public inquiry into the QEUH building.
Scottish Conservative leader Douglas Ross demanded a second inquiry into the oversight from SNP ministers.
Ms Sturgeon has previously argued that replacing the health board’s leadership would not "change overnight the practice in a hospital".
The health board has said it is fully committed to addressing any concerns.