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Thanks, Aghadowey. The health issue of a family member is looking a little better today so fingers crossed that trend continues.
I had an approximate birth year for Sarah Price (nee Flinn) from the 1901 census. Her age then was given as 13, so born around 1888. Can't access my home database from here, so I'm not sure whether or not I had confirmed that year with either her birth record or her age in the 1911 census.
Why William B Price came back at that time, it's hard to say, but visiting his mother would have been a good reason. His cousin, John Stanley Carter, a minister, returned to the UK for with his wife and sons in the 1950s for a visit, but I can't remember which year it was. John's mother, Frances Grace Stanley Carter (nee Price) also appeared on a passenger list coming or going to South Africa, but she was just visiting her son. John's family group appear on a passenger list visiting England. When he died in South Africa sometime later, John's will named four sons, who are possibly all still living so shall remain unnamed here.
The Moira Park address for William Price on the passenger lists suggests that someone in the family was still living there while the youngest William Price was in South Africa. It looks like they moved to Moira Park from Seacliffe road in 1942/43. I wonder if the Flamingo dance hall was one of the Gorse Lodge group's entertainment enterprises.

Yes, you're quite right, it's a common name, and without some other evidence it's guesswork. You can see why I got quite excited to come across an actual address!

Aghadowey, that link to Bangor directory was great to see! You are correct in thinking this William Price is connected to the others I have sought in the past, and was the brother of Emma Stanley Price. He shares his first name with his father (draper/silk merchant), his grandfather (excise man) and also his son (born 1920, occupation unknown).
From the names in the 1943 directory, in two separate households, I wonder if perhaps Sarah's husband William Price had died by then, as she is listed as head of the household. The William Price at a different address might be their son, who would have been about 24 years old and could have started a family of his own by then.
Since William's father (the draper/silk merchant) died in his early 40s and his grandfather (excise man) died in his mid-30s, I would not be surprised that this William Price died before he reached 60 years.
I've made a note of the house name, "Doonfeeny", which, you're right, wasn't mentioned in the mother-in-law's death notice.
Thanks! A few more clues to go on with.

I had a feeling that finding electoral registers wasn't going to be that easy. I'm oceans away from Belfast, so can't look in person.
Thanks for your efforts in searching deaths and wills. I had not found one either.
That's a great find with the newspaper item from 1942, though. I'll see whether Gorse Lodge Enterprises can lead me to anything else. It encouraged me to comb more carefully through the newspapers, and I found that the house on Seacliffe Road went up for auction in January 1945, with vacant possession. There is another news item saying that Mrs Price of that address won first prize at a flower show in 1938, so now I have located them in that place for a few years. 
Thanks, Elwyn!