Hi Rosie,
I'm not really that much further ahead of you, but I think I do have Robert's father and mother, I think they are Robert Gibson & Janet Gibson [possibly cousins] they were married on the 9th March 1825 in Tranent, East Lothian. On the OPR it states that Robert Gibson Hawker in Tranent married Janet Gibson daughter of Alexander Gibson Hawker in Falkirk.
I cannot find Anne Gibson's [Renwick] death recorded anywhere? But I do know that Robert remarried in
1896, he married Jean Francis in Haddington, on the marriage certificate his parents names were given as Robert Gibson [Hawker] and Jean Gibson [ms. Gibson] so I do think this is the same couple that were married in Tranent in 1825 as people with the name Janet often had their names shortened to Jane or Jean.
Robert died in Kirkaldy in 1917. His son Daniel registered his death and mistakenly gave Robert's mothers name as Mary Gibson.
My Grandmother also used to tell me off her and her sisters sitting in the back of her father James Gibson's horse and cart.