The law change was needed because Rowen fell between the cracks of New Zealand's adoption law.
She was born in 1993 with the help of an anonymous sperm donation to Ms Sullivan, a British citizen, and Doreen Shields, a New Zealander.
Ms Sullivan, a teacher aide, was registered as Rowen's birth mother.
The family moved to New Zealand when Rowen was 6 to give her a "Kiwi lifestyle" of climbing trees and riding her bike on uncluttered roads.
After a five-year battle with cancer, Ms Sullivan died in 2010.
A year later, when Rowen turned 18, she no longer had any legal connection to her other mother, despite Ms Shields being her parent since birth. The law did not allow two mothers to be recognised as parents of an adopted child.
Ms Shields planned to adopt Rowen, but this would require Ms Sullivan's name to be removed from her birth certificate - "a horrible thing to do", Rowen said.
At the time, Labour MP Louisa Wall's bill to legalise same-sex marriage was before Parliament. Ms Shields wrote to the Labour MP, asking for help.
Ms Wall found that the only way she could have both mothers' names on a birth certificate was to submit a private bill to Parliament.
"I had no idea that a private bill was even a thing," Rowen said. "When they told us that they had to literally rewrite the whole law [it] was quite a shock."
Ms Shields hesitated, wary of dragging her daughter into the public spotlight. But Rowen urged her on.
In her submission on the bill, Ms Shields said that the law was 'unspeakably cruel".
She said Rowen's birth certificate should reflect the truth of where she came from: "But her mum is missing from it, so it is a lie. Her mum never gave her up - never."
Rowen told the parliamentary committee considering the bill: "I want my mum's name on my birth certificate to honour her memory and what she means to me."
Despite an early blip, when New Zealand First opposed a law change, the bill progressed without controversy. After the third reading on Wednesday, Rowen and her mother drank champagne with Ms Wall and her partner Prue Kapua, who drafted the special legislation.
Rowen is now training to become an au pair and has a girlfriend of two years.
Asked about the influence of her parents on her sexuality, she said: "I don't really believe that I am dating a woman because I was raised by women.
"I think everyone is starting to realise that ... you can fall anywhere on the spectrum and people are starting to realise gender identity isn't so black and white."
The passage of her bill both increased and dented her faith in politics. On the evening on which MPs voted to help her family, National MPs also tried to filibuster a bill to increase paid parental leave entitlements.
"I didn't realise there was so much bullshit," Rowen said.
So how does it feel to have the law changed just for you?
"Very, very strange. You would never think you were special enough to be spoken for, so singled out, in something as important as Parliament," she said.
"A lot of [MPs] mentioned that they felt like wish-granters or fairy godmothers, being able to grant me that wish."
Law for one
Private bills usually affect companies, charities and trusts. But some focus on just one person or family:
The McLean Motor-car Act 1898
The act was one of the first to regulate the use of motor vehicles in New Zealand.
William McLean, a commission agent, had imported two Mercedes Benz vehicles and he promoted a bill which imposed a speed limit of 12mph (19km/h) and required motorists to carry bells to warn others and to use their lights half an hour after sunset and half an hour before sunrise.
Longley Adoption Act 1985
Ralph and Emily Longley obtained an interim adoption for two children, Lorraine and Leanne Chapman, in 1970. Their lawyer never made a final adoption order but this was not discovered until 1983.
A new adoption order could not be made because the parents had divorced, yet they were still in a good relationship and lived together. The private bill allowed them to adopt the children.
Stockman-Howe Marriage Act 1985
Thomas Stockman and Rosalina Howe were unable to marry because he was her mother's half-brother.
They had already lived together as man and wife for years and had four children, and the private act allowed them to marry.