I don't see a birth registration for an Amy (nor for an Emma) but I have found this and wonder whether this is the answer
1871 All born Wigan Lancashire
24 Spring Gardens, Wigan, Lancashire
Elizabeth Powis Head W 60
Ellen daur 32 Cotton Reeler
Henry son Un 28 Cotton Weaver
Hannah daur 22 Cotton Weaver
Emma Granddaur 7 Scholar
Nancy granddaur 2
James Nephew 25 Coal Miner
Joseph Gaskell Brother mar 59 Cotton Weaver
Thomas Gaskell Brother Unm 54 Cotton Weaver
RG10; Piece: 3889; Folio: 113; Page: 46
As Elizabeth's daughter and son are unmarried, could this be Joshua's child staying with her? I wonder if it's possible that somebody said to the enumerator in 1881 "Emmy" and it was written down wrongly as "Amy"?
Just to confirm that Joshua is Elizabeth's son, here is 1861 - All born Wigan, Lancashire
24 Spring Gardens, Wigan
Elizabeth Powis Head W 50
Thomas son Un 28 Night Watchman Iron Works
Richard son un 26 Cotton Power Loom Weaver
Ellen daur Un 22 Cotton Reeler
Joshua son un 20 Cotton Power Loom Weaver
Henry son un 18 Cotton Power Loom Weaver
Hannah daur 12 Scholar
Joseph Gaskell Brother Mar 49 Cotton Power Loom Weaver
Thomas Gaskell Brother Unm 45 Cotton Power Loom Weaver
RG9; Piece: 2777; Folio: 127; Page: 41
Strangely boarding next door with John and Elizabeth Fairhead and family is
Joshua Powis Mar 51 Waterworks Labourer born Wigan.