She said one way parents could avoid the latter was by identifying their values at a core level and what was important to them.
"To have a connection with your children will help them be resilient to the media spotlight and how a person parents with a lot of attention," she said.
"When a child does fail the parent should be there to comfort them and provide clear boundaries for them."
But Chadwick said the child wouldn't be the only person in the spotlight.
As a woman in power, Ardern also would be.
"Being in the spotlight when having leadership is something many women experience," she said.
"There are questions around the balance of family and work and raising a healthy baby and the relationship between mother and child when a mother has to work.
"The parents have to be able to figure out their strengths and weaknesses."