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i think we might need a little more evidence to allow us to home in on your twins. Are you saying that your great-grandmother had twins Jemima and Ina in 1901 surnamed Hart; that Jemima was adopted by someone called Thomson, and Ina died in 1963? Because I can't find anything to match that.
However in 1901 twins named Jemima Innes Thomson and Williamina Down Thomson were born in the district of Pitsligo in Aberdeenshire. The mother's maiden surname is omitted from the index, which usually implies that the birth was illegitimate.
There is a death of Jemima Innes Thomson or Ritchie or Collett in Pitsligo in 1963, so it was Jemima, not Ina, who died in 1963.
The original documents can be viewed at
www.scotlandspeople.gov.uk for a modest fee. Either of the birth certificates will tell you the full name of the twins' mother and where they were born. This may allow you to find their mother in the 1901 and earlier census.