On the 1861 census, father Ralph is a widower.
So, when he died, they would have been left as orphans?
1861: Reference RG09, Piece 3739, Folio 59, Page 16
Willington
Hope, Ralph Head Widower M 46 Carterman b Midlestone(?)
Hope, Johnson Son M 14 Horse Driver at Colliery b Seaham Halborn
Hope, Ann Daughter F 13 Scholar b Napping (?)
Hope, John Son M 5 Scholar b Bowes House
Hope, Mary Jane Daughter F 3 Scholar b Bowes House
Peacock, Margaret Servant Widow F 75 General Servant b Greystoke