He had also emailed mortgage company staff to say that if they did not get him "an interest rate I can afford" he would take his own life and "take yours with mine".
The emails escalated to threats to murder government employees and blowing up the Beehive.
When police arrived at the house soon after those threats, Tier resisted arrest and had to be handcuffed.
The court case appeared to trigger the incident on April 26 when he threatened the woman and children, and a policewoman who attended the incident.
Police prosecutor Steve Burdes told the Christchurch District Court that the eight-year-old girl had stood in front of her mother to try to stop her being hurt when Tier became angry and smashed a speaker and a glass ventilator system with a mop.
Judge Alistair Garland remanded Tier on electronically monitored bail for sentencing on September 28. He asked for a pre-sentence report and an assessment for home detention but he said that was not an indication of what the sentence would be for the serious offending.
He noted that defence counsel Margaret Smyth had begun the process of getting a psychological report done on Tier.
Tier pleaded guilty to 14 charges including several threats to kill and destroy property, resisting police, intentional damage, and assault.