Julie Horton says her ten-year-old daughter is having nightmares over their torment.
"One of the stones smashed through a window and just missed my daughter," said Mrs Horton, 36.
"Now she is having nightmares and often wakes up screaming ‘stones'.
"We've had to move her from the front bedroom to the back because she is afraid to sleep by herself anymore.
"We can't let her sit on the sofa either because it's by the window where stones have come through."
The family says their suffering started about four months ago.
"I've got a good 40 stones in a bag that I've kept," said Mrs Horton.
Her father John Goodyear, 54, added: "Every morning we have to go round and sweep them all up.
"A stone has come through our front door and also through the living room window.
"Sometimes we can go three or four days without any trouble, then all of a sudden we could be watching television and hear a smash and find a stone through the front door.
"Sometimes it's been happening in the middle of the night at 2.30am.
"We are all on tenterhooks wondering when it will happen next."
Mrs Horton, of Champion Way, Church Crookham, said: "I've rung the police at least 15 times but they say I've got to see these people or catch them doing it before they can do anything. But how can you see them when it's pitch black outside?
"I just can't see why the police can't do anything. When we were little, if we played knock-down ginger we'd be in trouble.
"They say they've got better things to do looking at all the pubs in Fleet Road.
"We've got two German Shepherds but we can't let them in the front garden in case anyone's out there.
"We're like prisoners in our own home."
Mrs Horton said she was due to raise the matter with MP James Arbuthnot during a surgery at Hart Council's headquarters in Harlington Way, Fleet, on July 4.
Insp Steve Coward of Fleet police said: "It is a problem and I do sympathise with her, but where do you start?
"The only way is to attach a police officer with her 24 hours a day and that's just not practical.
"We need to know where these stones are coming from, or a possible suspect."
Last month the News revealed how stone-throwing youths were making life a misery for pensioners living in Brookly Gardens, Fleet.