Mr Caldwell cited health and safety as reasons why Mr Tupe was not allowed on the slide with his daughter and said he was not being discriminatory.
"We get children who get hurt by other children playing on the slide so if we're going to let other adults up there all we're going to do is escalate the problem," he said.
Ms Hita took to Facebook after the incident, in an emotional post.
"We don't want to go on the slide - we have to, to make our daughter feel normal. There was a lot of swearing and I've said how embarrassed I was but I've never been in that situation before," she said.
Mr Caldwell said he threatened to call the police because of the language used.
"The rule is adults are not allowed on the slide - there are no exceptions."
He told the Northern Advocate he would be willing to come in early so that Phoeknix could use the slide without anyone else around.
However, Ms Hita said she was too upset by the incident and declined the offer.
Ms Hita said it was hard for her trying to give her daughter a normal childhood.
"It's my child and it's hard to see my child suffer, to be told she can't go on a slide, every kid wants to go down a slide."
Comments on the Facebook post, which has been shared more than 800 times, suggested boycotting Chipmunks Whangarei but Ms Hita said she did not want that to happen.
"I didn't want people to hate him, I didn't want people to stop taking their kids there because I will take my kids back there, just not yet," she said.