I am trying to find my ancestor, Frances Ann Smith, who was born in Wingate, Durham (Easington District) in the Sept qtr of 1869. She appears on the 1871 census in Wingate aged 1 with father Thomas, mother Jemima, and brothers George, Joseph, William and Valentine (RG10 4976 household 178). Her mother died in 1872 and her father remarried (well, he lived with someone he called his wife but I can't find a marriage record) and by 1881 the family are still in Wingate as follows:
Thomas Smith 49
Mary Ann Smith 55
William Smith 16
Valentine Smith 13
Frances Ann Smith 12
Sarah Ellen Smith 10
(RG11 4970 household 225)
I know that Frances had a baby in May 1885 though she gave it to relatives to bring up as their own (she would only have been 15 and single). The baby was born in Wingate so I know Frances was still there then but that's the last I can find of her! I've searched BMD's as well as all further available censuses, using all sorts of combinations and even just with County and year of birth but no name, and I'm not coming up with anything likely.
I am starting to wonder if perhaps she went off to America with her father and step mother in 1888 (Allegheny, Pennsylvania). Her sister, Sarah Ellen Wills also seems to have ended up there. I don't have a worldwide membership on my genealogy website subscription and am reluctant to buy one in case its a fruitless search. Any ideas, help or suggestions would be greatly appreciated!