"Rather, he has cursorily dismissed fundamental legal principles that provide for fair processes, and issued findings that seemingly accord with his predetermined view that is not supported by evidence", the letter claims.
It also criticised the coroner's decision to dismiss the views of a key expert instead of calling on him as a witness, which was "to the DHB's detriment".
White also claims the coroner had been communicating with Nicky's family on more than simple procedural issues, giving a "strong impression that this inquiry has not taken place in an impartial way".
In February, Nicky's family alleges they were blindsided when they received a letter from Crown Law in February that there had been a request for a new coroner.
Nicky's mother Jane Stevens said herself, husband Dave Macpherson and son Tony Macpherson-Stevens were "appalled at the DHB's aggressive attack on the coroner and the Inquest findings".
Stevens said there was no truth in the accusations, as the coroner had not had any private contact with them.
"The DHB's behaviour in this whole affair has been reprehensible, to say the least. It has devastated our family and significantly delayed our ability to find closure and have a chance to move on with our lives," she said.
"They don't like the fact that the coroner has run a very fair process and has come out with an answer that doesn't show them in a good light, so now they are using taxpayer-funded legal bullying to try to change the rules after the event to get a different outcome."
"Bain acted like a stone god at the coronial inquest. I'm not sure how you could accuse him of his conduct being questionable."
Nicky disappeared from the Henry Rongomau Bennett Centre at Waikato Hospital on March 9, 2015, after he was allowed out on unescorted leave against the express direction of his parents.
Three years after his death a coronial inquest was held in June 2018 and Coroner Wallace Bain ruled in December the 21-year-old took his own life "in the precise manner and place he previously said he would" and that Nicky's death was "avoidable".
He also said the young man's care fell "well short of what he and his parents would have expected".
Nicky's family is now seeking advice from its lawyers before putting in its own submission strongly disagreeing with the Waikato DHB.
The Herald has approached the Waikato DHB comment. Coroner Bain was unable to comment.