It was only after a private prosecution was filed and at least six unsuccessful appeals by Rangitonga to have the case thrown out that he admitted his guilt.
The 31-year-old solo mother said it still felt a "bit surreal" to finally succeed in getting some justice.
"But my daughter has hopefully come into the world which is a little bit better for me."
Ms Trainor said her other children, Azahria, 8, Ava, 7, Kaia, 5, and Levi, 3, were all present at the birth and were already besotted with the new baby.
Rocky, the family dog, was also very attentive, she said.
Ms Trainor said her greatest wish was to have her children, who had been through so much as she battled to get justice, be proud of her.
"And just like any other mother, I want my little girl and my other children to feel safe and loved, and grow up in a world where women are treated with the respect they deserve."
Ms Trainor said she knew she was going to have another daughter.
"I know I have had nine months to decide but choosing the right name is so important.
My other children kept telling me I should name her Blossom which is not helpful at all. "
"Maybe this is one occasion when Birth, Death and Marriages will allow me to call my new baby Justice," Ms Trainor quipped.