Working in the education sector herself, she believed schooling for her son Jaxon, 4, to be the most important consideration.
The family realised the mistake a few months after they had settled in at the end of 2010.
A set of neighbours were moving out - claiming that they were leaving so they could get in a better school zone.
Mrs Molloy rang the school the next day and was told even-numbered houses like theirs were disqualified.
Their previous house had already been in Ellerslie School's zoning, but Mrs Molloy had just recovered from cancer and there were unpleasant memories tied up with the townhouse.
And the new house had a yard - room for a trampoline and a place for Jaxon to play.
"It's heart-breaking," Mrs Molloy said. "We thought we were doing the right thing."
The issue reached the school's board of trustees and, eventually, the country's then-Secretary of Education.
The school's principal had been apologetic when he realised the mistake, Mrs Molloy said. The school's website was amended, though copies of the old document are still around on real estate websites.
The school tried to make an exception for Jaxon, but said its "hands were tied" unless the Ministry of Education allowed an amendment to the school zone or directed the school to accept Jaxon as a pupil.
In a letter to the family, board chairman Roger Windle said: "We are sorry that we cannot be of further assistance, and sincerely regret the difficulties that this matter causes you and your son.
"Again, we would be delighted to accept Jaxon as a pupil if the ministry enables us to do so."
Former Secretary of Education Karen Sewell wrote to the school, rejecting its proposal to add Mrs Molloy's house to the school zone.
"Although you suggest that the proposed amendment is 'minor' I am advised that Ellerslie is already managing the 'likelihood of overcrowding'," she said.
"As a consequence it would not be in the best interests of the school to expand the zone."
Mrs Molloy said she had received legal advice, but did not want to cause expense to the school.
In a statement to the Herald, a spokeswoman for the Ministry of Education said that "the onus is ultimately on the parent to ascertain exactly which [houses] are in the school's enrolment home zone.
"The parents could also have checked the zones with the Ministry of Education."
The couple are planning to send Jaxon to another Auckland school later this year.
The school is out of the zone but he was accepted by ballot.
Read more: Kickbacks costing parents