Barnett accused the woman of cheating on him and called her a liar when she denied it.
He threw her to the ground and stomped on her head several times before storming out.
Because of the attack, the mother and child left the area for Twizel, but they returned in November.
Barnett was waiting.
When he turned up at the victim's home, she got in the car in a bid to escape.
The defendant grabbed the keys from her, gripped her by the throat and pushed her back in the car seat.
Again, the woman moved house but it did not deter Barnett.
In December, he moved in with them, in violation of his conditions.
Just before Christmas, the defendant again flew into a drunken rage, questioning the victim's fidelity.
Seeing her texting someone, Barnett grabbed his partner's phone and smashed it on the floor.
He then grabbed the woman by the neck and ''squeezed tightly'', the court heard.
''During this their daughter was saying 'No, daddy, stop','' court documents said.
Barnett threw the woman backwards into a dishwasher and she slumped to the floor.
She could not breathe or move, Judge Kevin Phillips said.
When the victim came to, she crawled into the lounge where her daughter covered her with a blanket.
But the gesture of tenderness was swiftly turned into another attack.
Barnett took the blanket, put it over the victim's face and applied pressure until she was unable to breathe.
''So this is how you want it to be. You want me gone,'' the man said.
He abruptly left the house and smashed the woman's car windscreen on his way off the property.
Barnett declined to make a formal statement for police but conceded he ''mucked up''.
Judge Phillips said the victim had been too scared to leave her partner at the time but now was focused on a future without him.
''She is quite sure if you wanted to, you could have killed her,'' the judge said.
It was a ''major aggravating factor'', he said, that the couple's young daughter saw the violence.
Barnett was jailed for 21 months and ordered to pay the victim $592 within 90 days of his release from prison.
A protection order was also granted.