Edmonds and the woman had previously lived together for about two years with her two sons.
But in early 2014 they separated, with the defendant moving to Whanganui.
However, Crown prosecutor Alysha McClintock said it was clear the relationship was not over in Edmonds' eyes. He continued to pay money into one of her son's bank accounts, and kept up a stream of texts and calls, which the woman responded to a "limited extent".
In the 46 days leading up to the alleged murder, the defendant phoned and text the woman more than 200 times, which she responded to on "fewer and fewer" occasions, Ms McClintock said.
Mr Bettink was living with the woman by this stage, and on the morning of November 6 the Crown said Edmonds made the six-hour journey to Auckland after becoming suspicious his ex was seeing someone else.
He got to the woman's house to find Mr Bettink there looking after the boys while she was out collecting a takeaway dinner.
When she returned Edmonds pushed her over and the men fought.
"The attack lasted 40 to 50 seconds. There was no conscious appreciation by Mr Edmonds that what he was doing was likely to cause death, and [he] just carried on anyway," Mr Lance said.
"This was a spur of the moment reaction to Mr Bettink actually punching him and he overdid it, and he's sorry for that."
Edmonds will be sentenced next month.