Hartlepool Magistrates' Court heard that Lily Todd, 51, argued with her daughter on a Friday night.
She got the rabbit and started kicking it, while demanding her daughter went back inside the house. The rabbit ran off and a neighbour picked it up and took it to his home.
John Ellwood, prosecuting, said: "Her neighbour gave her back the rabbit and warned her that she shouldn't kick the rabbit.
"The defendant said that was the only way she could get her daughter in, and the only way she would listen to her.
"The neighbour said that it was not the rabbit's fault and the defendant then picked up the rabbit and threw it at the neighbour, stating that he should just have the rabbit."
Todd's neighbour took the animal back and alerted the RSPCA of the attack, who then collected the rabbit and took it to the vets. X-rays were carried out which showed that the rabbit had suffered five fractured ribs in the attack, two on the right side and three on the left.
Todd admitted losing her temper, but denied kicking the rabbit. She pleaded not guilty, but was found guilty of causing unnecessary suffering to a protected animal.
As well as being disqualified from owning animals for five years, Todd was given a 12 month community order with a requirement of supervision and ordered to pay £500 costs to the RSPCA.
John Relton, mitigating, said: "My client is a 51-year-old lady of previous good character who is in poor health. She owned two other animals, another rabbit which was in good health and a cockatiel which was also in good health.
"This was a singular attack born out of frustration."
Twinkle and two other pets owned by Todd have been taken into care by the RSPCA, which branded the attack 'awful'.
RSPCA inspector Kristina Raine said: "I am pleased with the conviction and the sentence passed. This was an awful attack on a small and defenceless animal."