Samantha Southall, 32, called the girl a “p*** c***” before threatening to smash windows of the house she was in, Derbyshire Live reports today.
The girl’s family had complained Southall had woken them in the middle of the night, a court heard.
When police tried to arrest the yob, she resisted and threatened to let one of her dogs loose on them.
She was eventually detained and taken into custody by police where she continued to be abusive to officers.
But on Monday, Southall was sentenced for a total of eight weeks, of which she will serve half, with the rest on licence.
Sentencing the woman at Derby Crown Court, Judge Jonathan Bennett said: “I cannot ignore this is an offence that causes a lot of anxiety for others, particularly for any on the estate where it took place.
“The sentence I’m about to give will be one of immediate imprisonment, but I have reduced it considerably.
“Sadly I come to the view that a lot of difficulties on that particular night were caused by the alcohol. You know that alcohol is a significant issue for you.”
Southall pleaded guilty to racially aggravated harassment, threatening to damage property and obstructing a constable in their duty.
The court heard Southall had been drinking on July 19 last year when she lost her mobile phone.
She was seen shouting at the property where the person she thought had taken the phone was staying, but this woke the 10-year-old girl and her family in Chaddesden, Derby.
Stephen Kemp, prosecuting, said: “The girl was awoken by the defendant shouting and said ‘shush, people are trying to sleep’. The defendant responded ‘shut you you p*** c***’.”
She then called relatives “fat b******”, threatened to smash the windows and “threatened to let one of the dogs she had with her off the lead” when police arrived.
In a victim impact statement read out at court, the girl Southall abused, who has an Indian father, said she was left “angry” after the incident, while her mum said that had played a part in the family’s decision to try and move house.
Southall was also on a suspended sentence for a previous offence which saw her assault a woman.
Simon Stevens QC, defending, said Southall had “significant” mental health issues including PTSD, anxiety, depression and possibly undiagnosed bipolar disorder.
He said: “She is one of ten siblings, only three of whom are still alive.
“There’s a significant amount of loss and difficulty this has caused her over the years. She has not had the opportunity to grieve for them.”