Nicole Barnes was at her home in Huyton, Merseyside, with her youngest child Delilah when she died on 3 October, the Liverpool Echo reported.
The 29-year-old was discovered by a friend who tried to resuscitate her until paramedics arrived.
The alarm was raised after her children’s school called her partner Craig Galloway to say they had not been collected.
As well as Delilah, she leaves behind three other children: Niamh, 10, Scott, seven and five-year-old Tom.
Her cousin Kim Jowett told the newspaper: “She picked up Delilah at 11.30am from nursery and was expected to pick her other children up later.
“She just passed away on the couch.
“She was an absolutely gorgeous young girl. She didn’t have a bad bone in her body.”
She continued: “She was one in million. She left such an amazing impression on everyone’s hearts and her children will never forget that.”
Ms Jowett has set up a GoFundMe page to help Mr Galloway, who she said has taken time off work to look after the children, including one who has severe special needs.
“Nicole was the most amazing mummy and her kids loved her so much,” Ms Jowett wrote in her appeal.
“She was a kind, loving beautiful person who just wanted the best for her kids.
“I’m just hoping we can raise a bit of money, however big or small to be able to ease the financial burden off Craig and the family, who are having to take time off work to look after the children at this difficult time.”
Ms Barne’s cause of death is not yet known, according to the newspaper report.