But after a 157km drive from Coromandel town, she ended up delivering him herself in her husband's ute in the Waikato Hospital carpark with her 3-year-old watching from the backseat.
Greene, 31, was three days past her due date when she started to feel pains in her stomach. But she had had Braxton Hicks (also known as sporadic practice contractions) so didn't think too much of it.
The pains were about seven minutes apart when she went to bed. By 11.30pm they started getting stronger so she and husband Steve decided to get on the road.
The closest hospital at Thames doesn't have a maternity ward so they needed to get to Hamilton, about a two-hour drive away.
"We wanted to get the drive done while I was still reasonably comfortable," Greene said.
"I still thought I had all the time in the world."
The couple deflated their birthing ball, packed up the car and woke up their son James.
But as soon as they got in the car, the contractions started getting stronger.
"We were quite excited, I started to think, 'We are definitely in labour. This is it'."
Coming into Thames, about an hour into the trip, the contractions were getting closer, about four minutes apart.
The couple thought it was time they call their midwife, who lives in Colville, a small town on the Coromandel Peninsula. She started driving to the hospital.
Just out of Thames, the contractions were about one minute apart and "very, very strong".
"I was not really talking anymore," Greene said.
"My little boy was copying my breathing and laughing at me ... I was a little bit worried he would be worried, that he would wonder why Mum was acting so weird."
Just outside of Morrinsville, Greene had a four-minute break from contractions.
"I just thought, 'I know this next one is going to be very, very strong'. I had the urge to push ... I just had to follow my body.
"My husband was saying, 'You're doing a great job, just keep breathing'. He was patting my leg.
"It's all a bit of a blur now but it was very, very painful and constant. I just had to keep breathing. I kept telling myself to chill out, my waters hadn't broken so 'he's not going to be born'.
"I could see the hospital, my husband pulled into the driveway and my waters broke."
After they pulled up to the maternity ward, Steve ran to the door to buzz for help.
But the baby couldn't wait. While his dad was trying to raise the alarm, Greene pushed once and his head came out. She pushed again and out came his body.
Tommy Michael Greene was born at 3.30am on January 24, weighing seven pounds and seven ounces (3.4kg).
The new mum of two pulled her newborn on to her chest and yelled out for her husband to come back.
"The absolute shock on his face of me just holding the baby and my little boy in the back just going 'baby, baby' ... it was pretty cool."
Steve adds: "I knew we were cutting it close but the last thing I was expecting to see was Anouska holding the baby."
The couple wrapped Tommy in a blanket and hospital midwives came running.
"They just said, 'Oh wow you did an amazing job'. They were calm, helped me out of the ute, into the wheelchair. It was so mental but just amazing. It was almost like you're in a euphoric state, once the pain had stopped. I was so proud of myself."
It was a totally different labour than the one with James, whose head became stuck. He needed to be born by emergency caesarean section after a ride to Waikato Hospital in an ambulance from the Thames Birthing Unit.
"Because this was a VBAC [Vaginal Birth After Caesarean], I should have been continuously monitored throughout the labour," Greene said.
"I was a little bit worried about all of that.
"But this was exactly what I wanted... everything was natural."
The family stayed at the hospital for the day as Tommy's blood sugar levels were checked before they were transferred to the River Ridge East Birth Centre in Hamilton.
They got back home on Wednesday.
As for the state of the ute? Green's father-in-law cleaned it for the couple and swears it "wasn't too bad".
