They are living quite close together, so possibly related
RG10/4110/fo 8
Beal Moor, Crompton, Oldham
John ROTHWELL,head,m,30,Self Actor Minder (Cotton)
Sarah Ann “ ,wife,m,29,
Sarah Alice “ ,dau,4,Scholar
William H “ ,son,1
All born Crompton
RG10/4110/fo 65
Beal Moor, Crompton, Oldham
Joseph ROTHWELL,head,m,52,Cotton P L Weaver
Mary “ ,wife,m, 57?
Mary Ann “ ,dau u,28,Cotton P L Weaver
Sarah “ ,dau,u,24,Cotton P L Weaver
Edwin “ ,son, u,23,Cotton Yarn Maker up
Emily “ ,dau,u,10 scholar
Alice “ ,dau,7
All born Crompton
There is also this family. This Alice was born Birkenhead, but probably lived in Oldham from a very early age.
RG10/4108/fo 47
Oldham Edge, White House, Royton, Oldham
Adam ROTHWELL, head,m,30,Boiler Maker, Lancs Heywood
Ellen “ ,wife,m,31,Lancs Heywood
William A “ ,son,u,7 Scholar,Kent Old Brompton
Alice “ ,dau,u,5,Birkenhead Cheshire
Elizebeth “ ,dau,u,2,Oldham
Jane “ ,dau,u,7m,Oldham
William “ ,lodger,u,25,Labourer,Lancs Heywood
Do you have a marriage certificate for Alice and Herbert? It should give the father's name and occupation which might help to identify her.