Have you been able to find any baptisms of Sarah daughter of Charles and Anne Goddard or her siblings in St Mary's at Troston? I can't find the baptism register for the period online. Perhaps they attended the Methodist Church in the area? Might also be worth looking for a baptism of Florence Goddard there too.
If this were my family I'd be almost convinced that Florence was the illegitimate daughter of Sarah, and that information Florence later gave on her marriage certificates and suchlike was a mixture of truth, information about her wider family, and tales. She certainly wouldn't have been alone in doing that.
There was a female GODDARD whos birth was registered Petworth reg dist, 1872, with no mother's maiden name. Have you been able to establish who that was or what happened to them? - incase Florence was born there, Sarah having been sent away or possibly staying with relatives?