Disclaimer: I've found an obituary for a Robert Gorman in Winnipeg but I can't say with any certainty that this is the correct person.
There was a Robert J. (Bob) Gorman who died 25 Feb 1972 at Misericordia Hospital in Winnipeg. The obituary says he was 59 years old, was born in Glasgow and came to Winnipeg at an early age which seems to match with the information you've provided. I see that ScotlandsPeople has a birth for a Robert John Gorman whose birth was registered in 1913 in Cathcart, Glasgow (the image can't be viewed but I believe you may be able to order a copy through their website) which is the same area where the marriage of Robert Gorman and Hannah McPhail McIntyre was registered.
If this is the correct Robert, his wife's name was Maude, he had a daughter Carol and he was buried at Chapel Lawn Memorial Gardens in Winnipeg. There was an obituary for Maude Louise Gorman who died 18 Mar 1988 in Victoria, British Columbia. It indicated she was predeceased by her husband, Robert and was survived by her daughter, Carol as well as her son-in-law Jamie Eakin and their daughter of Port Orchard, Washington. Some of her siblings are mentioned including one brother whose surname was Shaw. The Social Security Death Index has a death for a Carol A. Eakin who was born 31 Mar 1946, died 25 May 2002 and whose last residence was listed as Port Orchard, Kitsap County, Washington.
I found a transcript of an obituary at Ancestry for Carol Anne Eakin from the North Kitsap Herald which reads as follows:
Carol Anne Eakin, 56, a former resident of Port Orchard, died May 25, 2002.
She was born March 31, 1946 in Winnipeg, Canada to Robert and Maude (Shaw) Gorman.
She was a travel agent in Charleston, S.C. and was the former owner and operator of Advantage Travel in Port Orchard for 7 years.
She retired in 1997.
She is survived by her close friend R. Johnson* of Port Orchard and 8 grandchildren. There will be a private funeral.
Arrangements were handled by Pendleton-Gilchrist Funeral Home at Rill Chapel.
I haven't found a death for her husband Jamie but the Washington State Archives has some documents listed in their databases regarding the estate of James Eakin dated 1992.
I'm going to PM you with some other information. As I said at the start of the post, I can't say with certainty this is the correct Robert and family.
*If it is possible that a person is still alive I have just used their initial.
Jacquie