Yes, Caroline has certainly been quite a challenge!.
1861 Census - she was Caroline Matthews living in Lady Wood, Birmingham with husband(?) Lionell and daughter Eliza.
1871 Census - living at 40 Stoke St, St. Thomas, Birmingham as Caroline R Hawker and husband Daniel, with son George A Hawker and Richard Cooper (relative).
1891 Census as you said - 2 Spring St, Coventry
1901 at 120 Chester Road, Maccesfield, Chesire as Caroline Hawkes.
1911 with daughter Louisa Creed (nee White or Mills) at 55 Bryon st, Aston.
In 1881 I did found that Daniel Hawker/Hawkes was living with a daughter of Caroline's - Eliza/Elizabeth Davis (nee Matthews and not Daniel's daughter) at 12 Clifton Terrace, Lady Wood, Birmingham. No sign of Caroline or young George.
I also have Caroline's death in 1912, but I haven't purchased that certificate, but I would like to see if there was a death notice in the local newspaper. Are there any newspapers that give BDM at that time? Can they be accessed online?
Caroline always gave her place of birth as Stratford on Avon for all other Census. I have tried just about everything I can think of in 'searching' for her on various sites - so, since I've failed
, I have great hopes of asking for some professional advice to try and find her in 1881!.
Regards
Webby