I can find her with her parents in 1881, and on ancestry her father William is shown in detail along with his wife Eliza, the ancestry member does not have Sarah beyond 1881. However, on the 1891 census, William and Eliza have their infant grandson William Cox living with them, and he was born in Diddlebury, Shropshire, on the 1901 he is still living with his grandparents.
Now, that means that if he was born in Diddlebury his mother must have been there at the time! I have looked for a likely sarah unmarried and living in that area and as yet nothing really matches any detail you have. On the second childs birth certificate what is the place of birth?