Hi Mark,
It looks like her parents married in March quarter 1866 in Cheltenham district (Joseph Smith & Mary A Richings), if it's any use. If you can find (or buy) the full details of the marriage record, it would help a lot but it's not on freeReg and I'm not seeing it on FamilySearch. The full version of Louisa's christening record would likely also give Joseph's occupation, and so would any of the children's birth certificates.
This is the family in 1871:
https://www.familysearch.org/ark:/61903/1:1:V5YN-7ZH
This is them in 1881:
https://www.familysearch.org/ark:/61903/1:1:Q27J-V67F
In 1891 (probably):
https://www.familysearch.org/ark:/61903/1:1:W1TK-42M
In both 1871 & 1881, the mother is down as married not widowed, so I don't think Joseph was dead by 1871 even though he's not there. Particularly since there were more children born by 1881, although he could have died and they could have been illegitimate - I can't get on the GRO website right now to check mother's maiden name for them, the server's not responding. If they're illegitimate and the registrar knows that, he's supposed to put blank for her maiden name, but sometimes it doesn't happen that way in practice. The 1891 says Mary is a widow.
If Joseph was someone who travelled a lot for work, and it didn't make sense to drag his family along, like a sailor or a commercial traveller or a carter, he could easily have missed being at home for two censuses.
There's a chance Ann Smith who was boarding with them in 1871 was a relative, either a sister or mother of Joseph. I'm not spotting a good match for her on earlier censuses on FamilySearch, but if it was my family I'd definitely try harder to find her (trip to library to use Ancestry and FindMyPast).
Corinne
