I have justed posted quite a long reply, but the browser seems to have eaten it, so I will have to try again.
Malcolm Cheape recounted the story of Daisy Cheape in a post back in April 2005. She drowned off Mull when a small sailing boat capsized and she became entangled in a rope and couldn't escape. Malcolm also told how there was yet another death by drowning at sea in the same famlily.
The Gordon family seem to have all been involved in shipbuilding. William Gordon is described as a naval architect at the time of his marriage and his father, Aleaxander Milne Gordon, was a naval architect and engineer surveyor. Even the mother (whose name is difficult to read, but I believe is Euphenia Aitken Gordon formerly McIntyre) was described in the 1881 census as a ship tracer in Govan. I assume that this means that she made tracings of the drawings of ships, but I may have got this wrong.
I don't know about the story of money troubles. It is certainly true that Mrs Cheape was wealthy in her own right as she had inherited from her father, Richard Hemming, who had made his fortune in the needle industry in Redditch. Mrs Cheape did have a brother, but their father chose to leave much of his property to his daughter.
Like you, I wonder where Dorothy Robert was living between the 1901 census and her marriage in 1920. Did her father remain in England or return to the USA, and did he remarry? Whether Dorothy lived with her father or her mother, she must surely have received a good education. I suppose that we might learn a little more when the 1911 census becomes available, but apart from that we would need to find a living descendant who might be able to fill in some more of the story.
The online access to the Scottish records doesn't allow searches for births as recent as the 1920s, so if William and Dorothy Gordon did have any children I think that a trip to Edinburgh will be needed to find the information. I may be able to persuade my brother to have a look when he visits there this summer.
Nick