The mother, aged 25 and who has three children by different men, is adamant that she should be allowed to see her daughters, aged five and nearly four, so that they can retain their memories of her.
But on October 5 1995, Judge Beashel, sitting at Bournemouth county court, ordered that contact between them be phased out and, eventually, terminated altogether to free the girls for permanent adoption.
But in the civil court of appeal, Mr Justice Cazalet, sitting with Lord Justice Nourse, upheld the mother's case and overturned Judge Beashel's decision, describing it as 'ill-advised'.
'This was based on some severe bite marks and bruises which had been found on one girl's face in circumstances raising very serious concerns as to general neglect by the mother of the three children.'
All three children were taken into care and placed with foster parents, but the boy was allowed to return to live with his mother in November 1994.
By the time of the hearing before Judge Beashel one of the girls had had four different foster placements, and the other five.
'The mother, whilst not opposing the making of a care order, was resolute in her wish to continue to have contact with the two girls.'
But the girls' legally appointed guardian was equally adamant that their stability and security demanded that contact with their mother be terminated and that they be freed for adoption.
The judge added: 'All concerned were of the view that the boy and his two sisters should have continuing contact.'
He said Judge Beashel's decision that contact between mother and daughters be phased out before being terminated permanently was 'in any event ill-advised'.
Dorset CC is to re-apply to a different Bournemouth county court judge for her contact with her daughters to be terminated.
The girls have already been placed by the council with prospective adoptive parents and the appeal court judges ordered an 'expedited hearing' of the council's application.