Victoria Jones said her children, aged five and six, were 'distressed' following the media interest that accompanied their father's publicity stunt.
The boy and the girl are at the centre of a custody battle between Hatch and Jones, his ex-wife.
They live with their mother in Cheltenham, just yards away from their father's home.
In a statement released by Gloucestershire Police, Ms Jones called for the media to leave her family alone.
"We ask the media to leave us alone, not least because of the distress it is causing to the young people in our family, who have been unable to go to school today. Our family does not wish to and is unable to speak to the press on this matter due to ongoing legal proceedings," she said.
Hatch, 32, became involved with Fathers 4 Justice about a year ago because of the legal battle with his former wife over access to their children.
After the 18-month court battle, Hatch was granted one supervised visit every three months but claims to have seen them three times in the past three years and is waiting for a High Court hearing to apply for equal contact with the children.
He set up the Gloucester and Cheltenham division of Fathers 4 Justice before becoming national co-ordinator for direct action.