Hi Supernan
HAaving had a bit of a search around the 1871 census, it looks to me as if the family is split up in 1871. I think I've found Louisa working as a servant in Alverstoke but the only candidate for Annie is staying with her uncle and aunt James and Elizabeth Blackman in Havant. Does that make any kind of sense?
Anyway the details are -
Ref RG10/1125 Folio 56 Page 43 - Brockhampton, Havant
James Blackman - Head - Mar - 33 - Carter - East Meon, Hampshire
Elizabeth Blackman - Wife - Mar - 31 - Wife - Clandfield(?), Hampshire
Emily F Blackman - Dau - - 11 - Scholar - Hambledon, Hampshire
Florance Blackman - Dau - - 8 - Scholar - Havant, Hampshire
Anne L Nichols - Niece - - 5 - Scholar - Forton, Hampshire
Then Louisa -
Ref RG10/1149 Folio 127 Page 58 - North Lodge, Alverstoke
James Molesworth - Head - Mar - 42 - Chaplain HM Forces Active List - Aynhoe, Northamptonshire
Caroline M Molesworth - Wife - Mar - 40 - - Abingdon, Berkshire
Montague S Molesworth - Son - - 14 - - Gillingham, Kent
Constance M C Molesworth - Dau- - 13 - - Gillingham, Kent
Hugh S Molesworth - Son - - 11 - - Gillingham, Kent
Agnes M Molesworth - Dau- - 7 - - Ireland
Alice S Molesworth - Dau - - 6 - - Ireland
Arthur B Molesworth - Son - - 4 - - Alverstoke, Hants
Francis C Molesworth - Son - - 2 - - Alverstoke, Hants
Emily M K Molesworth - Dau - - 4 months - - Alverstoke, Hants
Louisa Nicholls - Servant - Mar - 26 - Nurse domestic - Charfield(?), HantsRosina Farr - Servant - Unm - 17 - Nurse domestic - Woolwich, Kent
Then I think we have Thomas here -
Ref RG10/1164 Folio 117 Page 50 - Parkhurst Barracks, Carisbrooke, Hants
Thomas Nichols - Soldier - Mar - 28 - Private 103rd Regiment - L???ston St Marys
Unfortunately some of the places of birth are very difficult to read. I would imagine that Elizabeth Blackman is Louisa's sister, judging by the similarity of birthplace name but it doesn't look like accuracy was a particular concern of some of the enumerators

Anyway, hope this helps
Angela