The woman could only see the child when supervised by family members, but later the little girl was sometimes allowed to stay at her home on weekends.
Things soured last year after allegations by the former hus-band about the mother's "inappropriate" behaviour towards their daughter.
He claimed she upset the child by making negative comments about her former husband and his family, and discussing "adult issues" relating to marriage and property.
He said the girl was at risk because of "sub-optimal" parenting.
A Family Court judge ruled the woman could only see her child at a formally supervised venue.
"I am concerned that the mother's approach to parenting ... led the court to hold real views [that the child could be at risk]," he said.
People who know the woman recently emailed the Ministry of Education, Teacher's Council and the university where she is enrolled about the situation.
They told the Weekend Herald it was highly alarming that she could be allowed to teach.
"We strongly believe this is now a matter of safety, and not morally right for [the woman] to have access to children, especially not in an authority position," they wrote.
"We are urging everyone not to allow her to take such a role as a teacher."
The university concerned refused to answer questions about the woman.
"The university says it doesn't discuss individual students publicly, but if it does become aware of any issues, the university raises them with the New Zealand Teachers Council."
Council spokesman Peter Lind said before any teacher was granted registration, they needed to demonstrate they had been satisfactorily trained to teach, were likely to be a satisfactory teacher, were of good character as evidenced by a police check and were fit to be a teacher.
"Therefore, before [the woman] can be provisionally registered, she will need to demonstrate to the Teachers Council that she is of good character.
"The onus of proof rests with the applicant," he said.
"Any graduate from a teacher education programme is required to apply for provisional registration before he or she can be employed in a teaching position in either a state, or integrated, or independent/private New Zealand school."
A Ministry of Education spokeswoman said schools were expected to do appropriate background checks before employing staff.
"Our first priority is the safety of students," she said.
The woman did not respond to the Weekend Herald.