Leah Biggs, 27, was told that having a baby could kill her because of her fragile heart - but gave birth to her tiny 4lbs 4oz daughter Aria last month.
However Leah, who underwent a heart transplant in 2010, suffered complications and had to be kept alive by a life support machine.
But after three weeks doctors eventually told her husband Mike, 28, there was nothing more that could be done.
Her sister-in-law Lucianna said: "It's such a difficult time for our family but Aria is pulling us all through."
Beauty therapist Leah, of Abercarn, Gwent, was born with a rare heart condition and received a heart transplant in 2010.
Doctors told her that her condition could kill if her she gave birth, but earlier this year she was was said to be thrilled at the prospect of becoming a mum.
In a Facebook post she wrote:
"I have achieved so much since my transplant and would hope I'm doing my donor proud. "By the end of this year I'll be a mummy and that was something I never thought would happen. "I have done more travelling in the last five years than my whole life and had my best friend/husband/soul mate and my rock by my side through thick and thin."
"Couldn't of come this far without either of them," she added. "So please remember heaven doesn't need your organs we do down here."Leah's family are now trying to help raise both money to help with Aria's upbringing, and raise awareness about organ donation.
"She was my reason for living and she/we wanted a child more than anything but we never thought anything like this would happen.
"I will never stop loving her and I hope she can look over and guide me and Aria." "We were the definition of love from the moment we met over 10 years ago and loved each other more and more each day and she didn't deserve this she was an amazing, kind, bubbly and positive person who put others first," she said. "The pain will never go but I have to try my best to do you proud by bringing Aria Leah-Ellen Biggs up the right way xx."
Doctors performed CPR for 40 minutes and managed to keep her alive by a life-support machine as her family were told Leah would need another heart transplant.
Leah came around briefly after giving birth under heavy sedation and called out to meet her daughter who was born seven weeks premature by c- section.
But Aria was being cared for by nurses in intensive care so she never got to see her daughter before she passed away.