Danielle Mason, 26, delivered her son, Rudy, on Saturday after going through three operations and two blood transfusions.
The sisters fell out four years ago after Jessie, 39, reportedly seduced Danielle's boxer lover, Tommy O'Neill.
A friend of the family told the Sun: 'Jessie was texting Danielle all through the 72-hour labour.
She is determined that this baby is going to heal the rift.'
Danielle's new baby - whose father is cage fighter Tony Giles - arrived three weeks early weighing 6lb 7oz.
She told the paper: 'Words just cannot describe how much I love him.
'He is the best thing that could have ever happened to me, the cutest little thing.
'I just can't wait to get him home from hospital.'
Danielle and Tony - who is from a traveller family - now plan to wed and are hopeful that Jessie will agree to be a bridesmaid.
Danielle said: 'I'm so hoping that I can be close to my sister again now. I'm sure she will love her little nephew.'
Jessie recently revealed how she too would like to have another baby with her new 50-year-old lover.
Did a new baby heal a rift in your family? Or do the reasons for the fallout always eventually resurface?