Leo and Luca Hallums were born at just 29 weeks due to complications caused by twin anemia polycythemia sequence (TAPS), a rare condition that occurs when there are unequal blood counts between the twins in the womb.
"The family have been going through a horrific time," said Emma Curtin, member of the family.
"When the babies came out, Luca was so swollen and really red and Leo was so tiny and pale.
"It was definitely touch and go for the first couple of weeks."
After several months in intensive care, baby Luca is now at home with mum Natalia and dad Ashley, but Leo remains in hospital fighting.
Despite numerous surgeries and blood transfusions early on, Leo suffered a devastating blow when he contracted severe necrotising enterocolitis: an illness that causes the bowel to become inflamed and die.
After another set of surgeries Leo is now on the mend, but the hardest part for his family is still only having one baby at home.
"It's been such a rollercoaster for Natalia and Ashley, for all of us," said Emma.
"It's been a lot of ups and downs, good days and bad days, but the hospital has been great with Leo and with Luca coming home."
Five months on, Leo has now been moved to the paediatric ward but is still under the watchful eye of staff at the LGI.
It’s a big step forward for the family, but Leo still has a way to go before he can be reunited with his brother.
“He is gradually putting weight on but he will be in hospital for a couple more months," explained Emma.
"Obviously it's is a lot of pressure on Natalia and Ashley, but the hospital has just been amazing."
For this family, the outstanding care that nurses, doctors and surgeons have given their two boys has been life-changing.
“We're so grateful for everything they have done for the boys; we're a small family and to lose anybody would be a huge hit, especially these babies.
The fundraiser is just a way to show the level of gratitude that we've got, and to try and help other people and families."
A Just Giving page has been set up to raise £27,960, the cost of the incubator needed for the LGI, with members of the family also completing the Yorkshire Three Peaks challenge in September to raise further funds.
To donate please go to justgiving.com/crowdfunding/leoandluca