Christine Morrison paid the price for her inability to control her sons, Alan, 18 and Lee, 19, when she was given just 28 days to quit her home.
Lord Justice May told the appeal court: 'The catalogue of quite appalling behaviour over a period of more than six years, with some intermissions, speaks for itself.
'To call it antisocial behaviour would be so far to understate it as to trivialise the effect it must have hade on the neighbourhood. It was more a reign of terror.
But recorder Hallam's decision at Newcastle county Court in October last year to allow Mrs Morrison to stay in her home had been 'plainly wrong', the judge ruled.
The brother's campaign of violence began in 1993 and lord justice May told the court they had, over the years, 'assaulted neighbours with fists, shovel handles, metal bars and knives'.
There had been incidents of 'witness intimidation, threats to kill, throwing bricks and stones at neighbours, starting fires, verbal abuse and criminal damage', he added.
The court had been given a five-page document detailing no less than 44 incidents of violence and intimidation committed by the brothers in the 17 months after June 1993, he said.
Some neighbours were so intimidated they were too scared to give evidence against the brothers, and others were so terrified they left the area, the court heard.
From October 1995 there was 'a lull' in the brothers' antisocial behaviour, but violence resumed in January 1997.
Their target was next door neighbour, Sam Cooper, who was 'brave enough to make himself available to give evidence'.
After enduring prolonged intimidation and death threats from the brothers, the local authority had to buy back Mr Cooper's former council home so he could move out of the area, said lord justice May.
Lee and Alan were on September 10, 1997, convicted by magistrates of violent disorder and three charges of witness intimidation and were sent to young offenders' institutions for six months.
Lee 'appeared to quieten down' after his period in custody, but Alan, who turned 18 in March last year, was undeterred. The judge read a litany of criminal convictions and incidents of violence involving Alan since his release.
Mrs Morrison's counsel, Charles Holland, told the court Alan was currently facing a charge of aggravated vehicle taking and 'anticipated' going to prison for six months.
Lord Justice May said Mrs Morrison was 'not herself a trouble maker' but neighbours were entitled to be protected from her sons who she seemed quite unable to control.
And he concluded: 'The balance of reasonableness, in my judgement, so obviously falls on the side which says it was indeed reasonable to make an order for possession that I consider the recorder was plainly wrong to conclude otherwise.'
Lady Justice Butler-Sloss and Lord Justice Robert Walker agreed the city council's appeal should be allowed and a possesion order made, giving Mrs Morrison 28 days to vacate the home where she has lived since 1989.
Lady Justice Butler-Sloss remarked that Mrs Morrison would lose her right to be rehoused if she is now declared 'intentionally homeless' by the council.
But she also has a seven-year-old son, Dale, and the judge said the council would have to give urgent consideration to his future.
'This woman has given birth to two very difficult sons who have caused a great deal of mayhem in the locality, but she also has a small son, and only can only pray he does not grow up like his brothers.'
Earlier Mr Holland told the court: 'I don't make any apology for my client's sons.'
But he argued a possession order would afford no protection to Mrs Morrison's neighbours as she could move next door into her father's home, or to private rented accommodation nearby, where her sons could continue to live with her.
Lee's behaviour, he said, had 'drastically improved' since 1997 and it would have been better for the council to seek an injunction against Alan to 'exclude' him from the locality.
Mrs Morrison had done all in her power to control her sons. She had at one point thrown Alan out of the house and, on another, had hidden his shoes in a bid to keep him off the streets.
'She cannot chastise Alan; she cannot lock him in his room,' he told the judges.