There was "pushing and shoving" until the woman was able to push him away. Jenkins fell down the stairs.
Dunedin District Court Judge Emma Smith said that was an opportunity for him to remove himself from the fraught situation - "and you did not do so, such was your rage".
Jenkins walked into the room where the victim had retreated with two children.
The altercation again became physical and "he grabbed the victim around the neck with his forearm across her throat".
Police described it in court documents as a "headlock".
"The victim attempted to fight the defendant off by kicking out at him, punching him and trying to bite him," they said.
The violence happened in front of the two kids, the court heard.
"They not only saw that, your 7-year-old child intervened, telling you to stop. How brave was she?" the judge said.
"You failed not only your victim, you failed your children terribly."
The court heard Jenkins was barred from living at the family home while he was on bail.
Judge Smith said the children sadly blamed his absence on themselves.
Defence counsel Sophia Thorburn said Jenkins was working two jobs to keep the family afloat financially.
The pair had argued before, she said, but things had never reached the point they did in September.
The judge was impressed by Jenkins' dedication to work and the "punishing regime" that followed but reminded him he was still responsible for helping at home.
"Sometimes it's hard to rouse yourself to do some of the work around the home. I don't care how tired you are, everything needs to be done at home.
"Try raising three kids and see how tired you get," she said.
Judge Smith considered community work for the defendant, but said she did not want to punish his family further by keeping him away.
Jenkins was sentenced to nine months' supervision.