James Macken, who also kicked the woman in the shins in anger after a failed attempt to install a washing machine, was jailed for two years.
The 22-year-old, of Queens Road, Donnington, Telford, was with the woman for two-and-a-half years, and developed a track record of controlling and abusive behaviour.
Shrewsbury Crown Court heard how she stuck with Macken even while he served a prison sentence, despite her sister's pleas to ditch him.
In July 2021, they were living separately, but Macken would spend lots of time at the victim's home.
A washing machine was delivered and Macken tried to install it but could not make it fit.
Philip Beardwell, prosecuting, said: "He smashed it, causing damage to the machine and he kicked her in the shins."
Later in the evening, Macken lost his temper again, punching the victim in the groin. She had only recently given birth.
On another occasion, the father of some of the victim's other children had attended her home unannounced. This angered Macken, and after the other man left, he headbutted the victim and punched her while she held a baby in her arms.
After that incident, she told him the relationship was over, and fled to a friend's house. But Macken went to the house later that evening, demanding to know where she was.
Police were called and he was arrested.
When he was interviewed by officers, he accepted there was a confrontation but insisted he "did not use excessive force", describing his attack as "a three out of 10".
The victim said in a statement that his behaviour left her worried for the welfare of her children who were "petrified" of him, and "ran upstairs screaming" when he came round.
Macken pleaded guilty to controlling and coercive behaviour. He has five previous convictions for five offences including violence and failing to comply with court orders.
Thomas Griffin, defending, said despite having young children, Macken lacks maturity.
"It is quite clear that he has problems and he accepts those problems," said Mr Griffin.
Judge Michael Fowler jailed Macken for two years, telling him: "You are 22 but you have already established a significant record of violent behaviour. I'm afraid I cannot avoid the seriousness of this behaviour."
The judge also made Macken subject of a five-year restraining order, banning him from contacting the victim.