From family search 1881 census (free census)   RG11/3592/26/46
Hannah Peterson, 29 b Liverpool, seaman's wife
Henry 7 b Wallasey
Olga M 5 b Wallasey
Sarah E 2 b Wallasey
address:   1 Shaftesbury Cottages, Wheatland Lane, Poulton cum Seacombe, Wallasey, Cheshire
Who was Hannah married to?    Possibly
from freebmd
Dec quarter, 1872, Birkenhead vol 8a page 747 (ref index)
APPLETON    Hannah       
PEDERSON    Otto     
SMITH    Elizabeth Agnes         
Tait    William
So it's looking very likely.