The 40-year-old woman, named by the newspaper as Louise Chantry, an unemployed holistic healer, was arrested on Wednesday after twice entering the exclusive Thomas's School in Battersea.
"She wouldn't have done any harm to George. He would have been safe with her. She just loves the royal family and loves kids," her mother Rhona Crawford, 75, was quoted by the paper as saying.
Crawford said Prince William, his wife Kate and their children George and Charlotte "represent the ideal family life she would like to have".
The mother said her daughter's obsession with the younger royals was similar to the public adoration for the late Princess Diana who died in 1997.
"It's a fairy tale. It's a fantasy," she said.
Chantry recently split from her husband after six years of marriage and has no children of her own.
She allegedly turned up twice at Prince George's school in 24 hours this week before being arrested.
Prince George is third in line to the throne after his grandfather Prince Charles and father William.
His formal title is Prince George of Cambridge but he is known as George Cambridge to his classmates at the £17,600-a-year (19,200-euro, $23,000) school in south London where he started last week.
Police said the arrest had sparked a review of security arrangements with the school.
"Police are part of the protective security arrangements for the prince and we will continue to work closely with the school, which is responsible for building security on its site," they said.