Aurelia was given a 5% chance of survival, but £17,000 was raised to bring her back for treatment.
Ms Jones said it was “surreal” to be home.
“Just being at home is quite hard to put into words, relief doesn’t quite do it justice but we need to look forward to the future,” she said.
“It was a waiting game as to whether we could get her home, it was very touch and go with her condition.”
Aurelia now needs an operation to reconstruct her nose after her septum was damaged in the hospital in Hanoi.
She also needs regular checks on her eyes as she has retinopathy, which can lead to blindness, as well as monitoring all the milestones until she is three years old to ensure she is developing well.
Premature babies with such small craniofacial surgery require specialised care, which the health system in Vietnam could not have provided.
Ms Jones said: “You were only ever given one option of something and sometimes told that they didn’t have the right equipment and you had to accept that. That was such a huge worry.
“I was counting down the seconds until we could get her back.”
After a 24-hour journey, travelling more than 62,000 miles, the family said they had not expected family and friends’ donations to cause such a “ripple effect” leading to help from strangers across the world including parents of other premature babies.
“That was very overwhelming,” Ms Jones said.
“The positivity and the love and support from afar was one of the things I think really kept us going. Being there feeling very isolated, very alone, it wasn’t easy for our family and friends either.
“It really made the difference between us being able to pull through some days.”